$($a$)$ Find the work done by the force $F(x,y)=\frac{-yi(x1)j}{(x1{)}^{2}4y^2}$ in moving a particle from $(0,1)$ to $(-2,1),$ then back to the $(0,1)$ along the parabola $y=2x^{2}4x1.$

$($b$)$ Evaluate ${}_S$curlF$*ndS,$ where $F(x,y,z)=zta{n}^{-1}(y^2)i{z}^{3}ln(x^{2}1)jzk$ and $S$ is the portion of the surface $z=1-x^2-y^2$ above the $xy-$plane, oriented upward.

$($c$)$ Let $F(x,y,z)=($:$y,-x,-z$:$)$ and $S$ be the boundary surface of the solid region $E$ enclosed by the paraboloid $z=x^2{y}^2-10$ and the plane $z=-1.$ Evaluate the flux of $F$ across $S.$