Swing/AWT/SWT :: Repaint Method Is Automatically Erasing Old Circle?

This code is shown to eliminate "smearing":

public void paintComponent (Graphics g) {
g.setColor(Color.white);
g.fillRect(0,0,this.getWidth(), this.getHeight());
g.setColor(Color.green);
g.fillOval(x, y, 40, 40);
}

I had done all the previous code (in my own style) and found that the background rectangle was either being redrawn on its own, or there was something else removing the old circles from the screen. I then typed in the code from the previous page exactly as it was, to see if I had some change in syntax that would cause this, and it did the same thing.

Here's my code:

import javax.swing.*;
import java.awt.*;
public class SimpleAnimation {
int x, y;
private static final int HEIGHT = 600;
private static final int WIDTH = 600;

[Code] .....

Is this because I'm using JRE7? I can't find any documentation that indicates the repaint() method has changed since Java 5.