Let $E$ be the intersection of the cylinders $x^{2}+y^{2} \leq 1, y^{2}+z^{2} \leq 1$. Compute the flux $$ \begin{align} & \iint_{\partial E} F \cdot d S \\[6pt] \text {where } & F=\left(x y^2+\cos (y z)\right) i-\left(x^2+\sin (z x) \right) j+(z+\cos (x y)) k, \text { and } \partial E \end{align} $$ is oriented outward.
Any one please help me how to solve it as I totally have no idea how to go with it.