Let $F(x,y)=(y^2+1,2xy)$

$($a$)$ Find $f(x,y)$ such that gradf$(x,y)=F(x,y).$

$($b$)$ Find the work done by the force field $F(x,y)$ along an arbitrary $($simple$)$ curve $C$ from $(1,1)$ to $(2,2)$