Differential Equation Problem in Graphs

The problem is this:

The graph of a function *f* passes through the two points p0 = (0, 1) and p1 = (1, 0). For every point P = (x, y) on the graph, the curve lies above the chord P0-P, and the area A(x) of the region between the curve and the chord P-P0 is equal to x^3. Determine the function *f*.

I'm having problems in setting it up. I believe it will be an integral of (f(x) - y(x), x, 0, x), where the y(x) will be the equation of the chord. But when I do y = mx + b to find y(x), using the point (x, f(x)), I end up with y(x) = f(x). SO i must be doing something wrong.

So any help will be appreciated. Oh, and this is in the defferential equation set, so i'm pretty sure i'm going to either use the first order differential or second order (both linear).