Double Integrals · Challenge problem

Let $f(x,y) = \dfrac{x - y}{(x + y)^3}$ on the square $0 < x \le 1$, $0 < y \le 1$. Evaluate the iterated integral $\displaystyle\int_0^{1}\!\left(\int_0^{1} f(x,y)\,dy\right)dx$, with the $y$-integral done first. (The solution also compares it with the other order.)