Calculate
$$ \iint_S Z ds $$
where $S$ is the surface whose sides $S_1$ are given by cylinder $x^2+y^2=1$, whose bottom $S_2$ is the disk $x^2+y^2$ is less than or equal to $1$ in the plane $z=0$, and whose top $S_3$ is the portion of the plane $z=x+1$ inside the cylinder.
I am not sure how to do this problem at all. I can somewhat visualize it, but I don't know how to proceed with this problem. How do I calculate this?