Do you have a basis for your series? Also when you mean fourier integral, what do you mean by that?
Typically a fourier series of some kind has a basis. The typical basis for periodic functions include the sine and cosine functions that are adjusted for offset and the periodicity of the function.
If you have this basis then you can use this to get the integral that takes a function to the fourier basis space and as a result, do the reverse (taking the basis back to an integral by using that connection).