Let R be the region bounded by the curves:

$\displaystyle y=x^2-1$ and $\displaystyle y=-x^2+1$

Verify Green's Theorem in the plane for:

$\displaystyle \oint_{\partial R} (y^2+x)dx + (xy+1)dy=\int_{-1}^{1}\int_{x^2-1}^{-x^2+1}-ydydx$

$\displaystyle \int_{-1}^{1}-\frac{(-x^2+1)^2}{2}-(-\frac{(x^2-1)^2}{2})dx=\int_{-1}^{1}0dx$

Umm... not sure if I was supposed to end up here.