Consider the vector field $F(x,y)=(2xy+e^y,x^2+x{e}^y+2y$:$)$ on $R^2.$

$($a$)(4$ points$)$ Show that F is conservative and find a potential function $f($i$.$e$.$ a function $f$ such that $F=$gradf $).$

$($b$)(6$ points$)$ Find ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr,$ where $C$ is the curve with parametric equations $x=t^2,y=t^2-t,0t1.$

$11$