$[\frac{-}{3\mathrm{.}07}$ Points$]$

Consider $F$ and $C$ below.

$F(x,y)=x^4{y}^{5}i+x^5{y}^{4}j$

$C$:$r(t)=($:$t^3-2t,t^3+2t$:$),0t1$

$(a)$ Find a function $f$ such that $F=$gradf.

$f(x,y)=$

$(b)$ Use part $(a)to$ evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ along the given curve $C.$