How to keep track of what I've previously draw

Question

They said:
Everytime the paint method is called, everything that was drawn before must be redrawn. The paint method has no way to keep track of what you've previously drawn, it is your responsibility as the programmer to keep track of such things.
Is this right?
How can keep track of my random shades of random amounts?
Is there a simple way to do that?
In a example, I must use getGraphics to get JPanel's graphics, then I use it to random draw something in the JPanel.
I just want to keep them in my JPanel when it resizes.I haven't get the answer yet.
Can you help me?

Answer 1

Ok I haven't got time to write the code for you, but here's the idea:
//User drags mouse around to draw on screen
//use mouseActionListener to catch MouseDragged event
int x = mouseEvent.getX();
int y = mouseEvent.getY();
Point p = new Point(x,y);
arrayListOfPoints.add(p);
// end mouse action capture
//override paint method of component
public void paint(Graphics g){
    super(g);
    Iterator it = arrayListOfPoints.iterator();
    while(it.hasNext()){
        Point p = (Point)it.next();
        g.drawLine(p.getX(),p.getY(),p.getX(),p.getY())