Evaluate the surface integral S F dS for the given vector field F and the oriented surface S. In other words, find the

Evaluate the surface integral ʃ_S F • dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.

F(x, y, z) = y j - z k, S consists of the paraboloid y = x² + z², 0 < y < 1, and the disk x² + z² < 1, y = 1