Let vec$(F)=($:$y^2,2xy$:$).$

$($a$)(10$ points$)$ Evaluate ${\displaystyle \underset{c}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r),$ where $c$ is the curve given by vec$(r)(t)=($:$t+1,t^2$:$)$ from $t=-1$ to $t=2.$

$($b$)(8$ points$)$ Find a potential function for vec$(F),$ and use it to evaluate the integral in part a$).$