i.10.1 Flux of the vector field

\( \underline{\mathrm{y}_{\text {word: }}} \) Find the flow of the vector field \( F \) through the surface \( S \) bounding the finite volume. Check the result using the Ostrogradsky-Gauss formula. \[ \begin{array}{l} F(x, y, z)=(x+z) z i+x^{2} j+(x-1)(x-z) k, \\ S:\left\{\begin{array}{c} x+z=1, x=0, y=0, z=0 \\ x+y=1 \end{array}\right. \end{array}\]