Evaluate the line integral

I = (x2z + yzexy) dx + xzexy dy + exy dz

where C is the arc of the ellipse r(t) = (cost,sint,2−sint) for 0 <= t <= PI.

[Hint: Do not compute this integral directly. Find a suitable surface S such that C is a part of the boundary ∂S and use Stokes’ theorem.]

Because this is from 0 to Pi, this is an open curve? Can you compute the integral using stokes theorem over the surface from 0 to 2Pi, so you have a closed curve and then divide that answer by two to get the open curve 0 to Pi?

I'm confused on what techniques to use when the curve is open.

any help would be wonderful. Thanks in advance!