Verify Stokes' Thm for the vector field v(x,y,z)=xi+zj-yk and the oriented surface S E R^3?

S is the half of the sphere of radius with y>0. The surface is oriented so that the y component of its normal is negative. I was able to get 0 for the curl dotted with the normal dS portion of the theorem. I am confused about how to verify the other side of the theorem.