Let $F=e^{xy}i+xj.$ Compute the line integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ along the square with vertices $(0,0),(0,2),(2,2)$ and $(2,0)$ oriented counterclockwise.

$0$

$\frac{13+e^4}{2}$

$\frac{3+e^4}{2}$

$\frac{3-e^4}{2}$

$\frac{13-e^4}{2}$