Java clears screen when calling paint method - how to avoid that?

I'm trying to draw two lines in a Canvas in Java, calling two methods separately, but when I draw the second line, the first one disapears (Java clears the screen). How can I avoid that? I want to see the two lines. I've seen paint tutorials (how to make a program like the Paint on Windows) where the user uses the mouse to draw lines and when one line is drawn, the other do not disappear. They just call the paint method and it does not clear the screen.

I'll be grateful if anyone can help me. Thanks.

View Class

import java.awt.BorderLayout;
import java.awt.Canvas;
import java.awt.Color;
import java.awt.Graphics;

import javax.swing.JFrame;

public class CircuitTracePlotView extends JFrame {


    private CircuitTracePlot circuitTracePlot;

    public  CircuitTracePlotView() {


        this.setDefaultCloseOperation(JFrame.DISPOSE_ON_CLOSE);
        this.getContentPane().add(circuitTracePlot = new CircuitTracePlot(), BorderLayout.CENTER);
        this.pack();
        this.setSize(250,250);
        this.setLocationRelativeTo(null);

        this.setVisible(true);
        circuitTracePlot.drawLine();
        circuitTracePlot.drawOval();
    }


}

class CircuitTracePlot extends Canvas {

    private final static short LINE = 1;
    private final static short OVAL = 2;
    private int paintType;

    private int x1;
    private int y1;
    private int x2;
    private int y2;

    public CircuitTracePlot() {
        this.setSize(250,250);
        this.setBackground(Color.WHITE);

    }

    private void setPaintType(int paintType) {
        this.paintType = paintType;
    }

    private int getPaintType() {
        return this.paintType;
    }

    public void drawLine() {
        this.setPaintType(LINE);
        this.paint(this.getGraphics());
    }

    public void drawOval() {
        this.setPaintType(OVAL);
        this.paint(this.getGraphics());
    }

    public void repaint() {
        this.update(this.getGraphics());
    }

    public void update(Graphics g) {
        this.paint(g);
    }

    public void paint(Graphics g) {
        switch (paintType) {
        case LINE:
            this.getGraphics().drawLine(10, 10, 30, 30);            
        case OVAL:
            this.getGraphics().drawLine(10, 20, 30, 30);
        }


    }


}

Main class

import javax.swing.SwingUtilities;

import view.CircuitTracePlotView;

public class Main {

    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {
            public void run() {
                CircuitTracePlotView cr = new CircuitTracePlotView();
            }
        });
    }
}

• You almost never should call paint(...) directly. I can count the times that I've needed to do this on one hand.
• Do not get a Graphics object by calling getGraphics() on a component as that will return a non-durable Graphics object. Instead either draw in a BufferedImage and display that in the paint method or draw in the paint method (if AWT).
• Since this is a Swing GUI, don't use an AWT component to draw in. Use a JPanel and override the paintComponent(...) method, not the paint(...) method. Otherwise you lose all benefits of Swing graphics including automatic double buffering.
• The super.paintComponent(g) method should be called in the paintComponent(Graphics g) override, often as the first method call inside of this method. This lets the component do its own housekeeping painting, including erasing drawings that need to be erased.
• Read the tutorials on Swing graphics as most of this is all well explained there. For e.g., please have a look here:
  • Lesson: Performing Custom Painting
  • Painting in AWT and Swing

Edit

• To have your images persist, I suggest that you draw to a BufferedImage and then display that Image in your JPanel's paintComponent(...) method.
• Or another option is to create a Collection of Shape objects, perhaps an ArrayList<Shape> and fill it with the Shapes you'd like to draw, and then in the paintComponent(...) method cast the Graphics object to a Graphics2D object and iterate through the Shape collection drawing each shape with g2d.draw(shape) as you iterate.

Since Trash posted his code,...

import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import javax.swing.*;

public class CircuitTracePlot2 extends JPanel {

   private static final int PREF_W = 250;
   private static final int PREF_H = PREF_W;

   private int drawWidth = 160;
   private int drawHeight = drawWidth;
   private int drawX = 10;
   private int drawY = 10;
   private PaintType paintType = PaintType.LINE;

   public CircuitTracePlot2() {

   }

   @Override
   public Dimension getPreferredSize() {
      return new Dimension(PREF_W, PREF_H);
   }

   public void setPaintType(PaintType paintType) {
      this.paintType = paintType;
      repaint();
   }

   @Override
   protected void paintComponent(Graphics g) {
      super.paintComponent(g);
      if (paintType == null) {
         return;
      }
      switch (paintType) {
      case LINE:
         g.drawLine(drawX, drawY, drawWidth, drawHeight);
         break;
      case OVAL:
         g.drawOval(drawX, drawY, drawWidth, drawHeight);
         break;
      case SQUARE:
         g.drawRect(drawX, drawY, drawWidth, drawHeight);

      default:
         break;
      }
   }

   private static void createAndShowGui() {
      final CircuitTracePlot2 circuitTracePlot = new CircuitTracePlot2();

      JFrame frame = new JFrame("CircuitTracePlot2");
      frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
      frame.getContentPane().add(circuitTracePlot);
      frame.pack();
      frame.setLocationByPlatform(true);
      frame.setVisible(true);

      int timerDelay = 2 * 1000;
      new Timer(timerDelay , new ActionListener() {
         private int paintTypeIndex = 0;

         @Override
         public void actionPerformed(ActionEvent arg0) {
            paintTypeIndex++;
            paintTypeIndex %= PaintType.values().length;
            circuitTracePlot.setPaintType(PaintType.values()[paintTypeIndex]);
         }
      }).start();
   }

   public static void main(String[] args) {
      SwingUtilities.invokeLater(new Runnable() {
         public void run() {
            createAndShowGui();
         }
      });
   }
}

enum PaintType {
   LINE, OVAL, SQUARE;
}