Check if Download Manager downloaded the file

How can I check if file has been downloaded and run its installation? I have a code:

public void downloadUpdate(String url){

    DownloadManager.Request request = new DownloadManager.Request(Uri.parse(url));
    request.setDescription("Downloading...");
    request.setTitle("App Update");
    request.allowScanningByMediaScanner();
    request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);

    String name = URLUtil.guessFileName(url, null, MimeTypeMap.getFileExtensionFromUrl(url));

    request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, name);

    DownloadManager manager = (DownloadManager) getSystemService(Context.DOWNLOAD_SERVICE);
    manager.enqueue(request);
}

To check whether the download manager downloaded the file, you must implements your BroatcastReceiver.

@Override
public void onReceive(Context context, Intent intent) {
    String action = intent.getAction();
    if (action.equals(DownloadManager.ACTION_DOWNLOAD_COMPLETE)) {
        DownloadManager.Query query = new DownloadManager.Query();
        query.setFilterById(intent.getLongExtra(DownloadManager.EXTRA_DOWNLOAD_ID, 0));
        DownloadManager manager = (DownloadManager) context.getSystemService(Context.DOWNLOAD_SERVICE);
        Cursor cursor = manager.query(query);
        if (cursor.moveToFirst()) {
            if (cursor.getCount() > 0) {
                int status = cursor.getInt(cursor.getColumnIndex(DownloadManager.COLUMN_STATUS));
                if (status == DownloadManager.STATUS_SUCCESSFUL) {
                    String file = cursor.getString(cursor.getColumnIndex(DownloadManager.COLUMN_LOCAL_FILENAME));
                    // So something here on success
                } else {
                    int message = cursor.getInt(cursor.getColumnIndex(DownloadManager.COLUMN_REASON));
                    // So something here on failed.
                }
            }
        }
    }
}

However, I am not sure whether you can install the APK programmatically. For security reason, I don't think you can. For application update, I think you should use google versioning control. When you re-deploy your app using different version number, the users should able to update automatically (unless user turn off at google play). Hope that this will help.

Update

You do not need to call the method that I mention. You just need to declare your broadcast receiver at your manifest xml file and DownloadManager will call at when download complete. The xml look something like below:

    <receiver
        android:name=".BroadcastReceiver"
        android:enabled="true"
        android:exported="true" >
        <intent-filter>
            <action android:name="android.intent.action.DOWNLOAD_COMPLETE" />
            <action android:name="android.intent.action.DOWNLOAD_NOTIFICATION_CLICKED" />
        </intent-filter>
    </receiver>