Vector Calculus · Challenge problem

Let $E$ be the solid cylinder $x^2 + y^2\le 1$, $0\le z\le 3$. Find the outward flux of $\mathbf F = \left(x + \sin(yz),\; y + e^{xz},\; z^2\right)$ through the entire boundary of $E$. Give your answer in terms of $\pi$.