Let R be a region bounded by the curves:

$\displaystyle y^2-x-1=0$ and $\displaystyle y^2+x-1=0$

I want to verify Green's Theorem in the plane for:

$\displaystyle \oint_{\partial{R}}(y^2+x)\, dx +(xy+1)\, dy$

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For the line integrals part, since the two curves intersect at (-1,0) and (1,0).

Can I use:

$\displaystyle \int_{0}^{0}(y^2+x)\, \frac{dx}{dy} \, dy + (xy+1) \, dy$

In which case they will both be equal to zero and I won't have to integrating?