Verifying divergence theorem with an example

[grissom]

Verify the divergence theorem when F=xi+yj+zk and sigma is the closed surface bounded by the cylindrical surface x^2+y^2=1 and the planes z=0, z=1.

I've done the triple integral side of the equation and got 3pi but don't know how to solve the flux side of the equation $$\oint\oint$$F.ds.

Any help is appreciated. Also, this is my first time using this, so the symbols may be a bit off.

 

[Fightfish]

You have to break up the cylindrical surface into three parts: the top, bottom and the "sides" for the lack of a better word. Then, perform the integral of F over each surface and finally, sum them up.