Hi, can anyone please help me with this question?

Let S be the capped cylindrical surface given by the union of the two surfaces

S1:

S2:

Let . Evaluate using

(a) an appropriate line integral

(b) the simplest surface for S

I have been working on this question for a long time.

For part (a),I parametrized line which is the circle, then put in vector field F and then dotted with velocity vector, and integrate t from 0 to , but I don't know what happened, I always end up 0!

For part (b),clearly the simplest surface would be the circle, but I still could not set up integrals and find proper normal vector.

Can anyone please help me and show me the details? Thanks a lot.