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 ʃʃ_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) = xy i + yz j + zx k, S is the part of the paraboloid z = 4 - x² - y² that lies above the square 0 < x < 1, 0 < y < 1, and has upward orientation