I'm stuck with a oriented surface integrals question...

I don't know how and where to begin...

The question's asking to evaluate the surface integral $\displaystyle \mathop\int\int\limits_{\hspace{-15pt}S} \vec{F}·d\vec{S}$ for the given vector field $\displaystyle \vec{F}$ and the oriented surface S. In other words, find the flux of $\displaystyle \vec{F}$ across S. For closed surfaces, use the positive (outward) orientation.

(sorry, this is just for my own reference to refer on later on)Q29. Pg 1092

$\displaystyle \vec{F}(x,y,z) = x^2\vec{i}+ y^2\vec{j}+ z^2\vec{k}$, S is the boundary of the solid half-cylinder $\displaystyle 0\le z\le \sqrt{1-y^2}$, $\displaystyle 0\le x\le 2$

How should I think of this question and where to start? Which formula to use? What are the boundaries and how did you find the boundaries?

Please help me~