4.* Verify Green's Theorem in the plane for $\oint_C [(x^2 - xy^3)dx + (y^2 - 2xy)dy]$, where $C$ is a rectangle with vertices at $(-1, -2)$, $(1, -2)$, $(1, 1)$ and $(-1, 1)$. [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for $y$ in terms of $x$ for each part - you should then be able to simplify the integrals.] [10]