Stokes' Theorem

[nicobautista1]

Hello, I'm a sophomore in college. The question I have is regarding stokes theorem. I understand it is: int (F dr) = int (curl(F) dS). My question is when do I use which. I am a bit confused, I see some exercises where I take the curl and dot it with the cross product of r, and some where I just take the vector function and dot it with dr.

Thank you for your help.