Suppose $f(x,y)$ is a bounded harmonic function in the unit disk $D = \{z = x + iy : |z| < 1 \} $ and $f(0,0) = 1$. Show that $\iint_{D} f(x,y)(1 - x^2 - y^2) ~dx ~dy = \frac{\pi}{2}.$
I'm studying for a prelim this August and I haven't taken Complex in a long time (two years ago). I don't know how to solve this problem or even where to look unless it's just a game with Green's theorem-any help? I don't need a complete solution, just a helpful hint and I can work the rest out on my own.