Is there a way to geometrically prove how the y-axis of the anti derivative of a function, f(x), represents the area under f(x)?. I understand that the area can be represented by the summation of ifinitesimal rectangles under the curve. I also understand instantaneous differentiation.

Is it because the y-axis of the anti derivative represents the summation of little dy's (change in y).

I've seen a proof that shows integration is the opposite of differentiation but why does it give area?