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) = y i + (z - y) j + x k, S is the surface of the tetrahedron with vertices (0, 0, 0), (1, 0, 0), (0, 1, 0), and (0, 0, 1)