Calculate AUC manually without using any Numpy or Sklearn library

I have given a set of X, Y coordinate and I need to find the AUC using trapezoidal formula, without using any numpy or sklearn library.

(x0,y0) is always (0,0)
(xn,yn) is always (1,1)

Below diagram

Without using any sklearn library, I understand I need to find below

hi = ?
wi= ?
AUC = sum (hi * wi)

Now I am not sure how to find hi, wi. I don't think I have all the necessary data to do the high school math. Am I missing something?

The area below (x1, y1) and (x2, y2) (as below vertically, not "diagonaly" like you seem to try to calculate) is simply:

(x2 - x1) * (y1 + y2) / 2 

You can then generalize to other consecutive indices and add all the terms with a for loop.

Normally AUC contains the area of the bottom right half (below your red dashed line) but if you need to take that off, just subtract 1/2 to your final result.

And you might also need to consider the edge case... not sure how you are supposed to consider before the sections between 0 and x0 and between xn and 1...