Vector Calculus · Hard problem

Let $D$ be the annulus $1\le x^2 + y^2\le 4$, and let $\partial D$ be its boundary with the positive orientation (outer circle counterclockwise, inner circle clockwise). Evaluate $\displaystyle\oint_{\partial D} -x^2y\,dx + xy^2\,dy$. Give your answer in terms of $\pi$.