Please help me in this math project!

I want to calculate this integral:

with S is the surface (point to outside) limited by the planes: z=4-y^2,z=0,x=0,x=1 using the Ostrogratxki-Gauss equation.

How can I do that? Please give me some example code.

I'm in hurry, so I hope to receive your answer soon. Your help will be really appreciated.

Thank you so much!