How are surface integrals calculated, namely the flow through a certain figure?

Question

Mathematics

I have a cube, from the origin to angles at points equal to one, how to calculate directly the flow through this cube?
Given: cube, vector field F(x^2-z, z+y, xy)
Solution:
1. Through the Ostrogradsky-Gauss formula, I sort of calculated, that is,
TripleIntgeral(divF)dxdydz = TripleIntgeral((x^2)' + (z+y)' + (xy)')dxdydz = TripleIntgeral(2x + 1 + 0)dxdydz = Integral(2x+1)dx*Integral(dy)| {0 <= y <= 1}*Integral(dz)| {0 <= z <= 1} = Integral(2x+2)dx = x^2| {0 <= x <= 1} + x| {0 <= x <= 1} = 1 + 1. The result is 2