Do the six faces separately. On the face x= 1, oriented outward. y goes from -1 to 1, z goes from -1 to 1. so that and the integral over that face is .
Do the same for the other 5 faces, x= -1, y= 1, y= -1, z= 1, z= -1.
Do the six faces separately. On the face x= 1, oriented outward. y goes from -1 to 1, z goes from -1 to 1. so that and the integral over that face is .
Do the same for the other 5 faces, x= -1, y= 1, y= -1, z= 1, z= -1.