Find $\int\int_S (\nabla \times F)\cdot dS\;$ where $F(x,y,z)= (zx+z^2y+x,z^3yx+y,z^4x^2)$.Let $S$ be the capped cylindrical surface given by the union of two surfaces $S_1$ and $S_2$ where
$S_1$ is $x^2+y^2=1, \; 0\leq z \leq 1 \;\;$and
$S_2$ is $x^2+y^2+(z-1)^2=1,\; z \geq 1$
$\nabla \times F = (-3yxz^2,x+2zy-2xz^4,z^3y-z^2)$
I don't know even know where to start. Any help would be really appreciated!