i.10.2 Flux of the vector field

condition: Find the flow of the vector field \( \vec{f} \) through the closed surface \( (\Omega) \) : \[ \begin{array}{l} \vec{f}=3 x^{2} \vec{\imath}+2 x^{2} y \vec{\jmath}+(2 x-1) z \vec{k} \\ \Omega: x^{2}+y^{2} \leq 1, \quad z \geq 0, \quad z \leq 1 \end{array} \]