If you only need to integrate the spectrum, you can generate a scaling array to multiply the output of the FFT. Assuming your FFT output is magnitude (as opposed to power) and linearly scaled (as opposed to dB), the scaling array looks like the following for single integration:
[0, 1/w_1, 1/w_2, ..., 1/w_last] where w_i = 2 * pi * f_i and f_i = df * i (assuming f0 = f_0 = 0) You can square each element of the scaling array to perform double integration.
