I have a question about a problem involving Stokes' theorem

The question goes as follows:

Use Stokes' theorem to evaluate:

Double integral of the curl of F dot n ds

Where S is the part of the cylinder z = 1 - x^2 for 0<=x<=1, -2<=y<=2 and F(x, y, z) = xyi + yzj +xzk

So far I have the Curl of F is equal to -yi - zj - xk. I am now completely lost. Any help would be appreciated, thank you.