Verify Green's Theorem by evaluating both integrals
$\int_C y^2 dx + x^2 dy = \iint_R \left(\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\right) dA$
for the given path.
C: rectangle with vertices (0, 0), (4, 0), (4, 7), and (0, 7)
$\int_C y^2 dx + x^2 dy = $
$\iint_R \left(\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}\right) dA = $
