Verify Green's Theorem by evaluating both integrals

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}{y}^{2}dx+x^{2}dy={\displaystyle \underset{R}{\overset{\phantom{}}{}}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{\text{d}\text{e}\text{l}\text{N}}{\text{d}\text{e}\text{l}\text{x}}-\frac{\text{d}\text{e}\text{l}\text{M}}{\text{d}\text{e}\text{l}\text{y}})dA$

for the given path.

$C$ : square with vertices $(0,0),(4,0),(4,4),(0,4)$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}{y}^{2}dx+x^{2}dy=$

${\displaystyle \underset{R}{\overset{\phantom{}}{}}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{\text{d}\text{e}\text{l}\text{N}}{\text{d}\text{e}\text{l}\text{x}}-\frac{\text{d}\text{e}\text{l}\text{M}}{\text{d}\text{e}\text{l}\text{y}})dA=$