Use Green's theorem for circulation $to$ evaluate the line integral $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r).$

vec$(F)=($:$(x{y}^2+2x),(2x+y^2)$:$)$ and $Cis$ the positively oriented boundary curve $of$ the region bounded $byy=1,y=2,$

$y=-2x,$ and $x=y^2.$