Most of the time, after you use an fft
alogorithm, you'll have a spectrum
(or if you look at the modulus squared
of your fft because your orginal function wasn't symmetric
and you have a complex fourier transform
) with its DC components at the very left and right ends of your scale.
So there's a nifty function included in most software packages that include fft algorithms -- the fftshift. It takes the right half of your fft and exchanges it with the left half. Now what you have is as close as you can get to what you would find if you integrated by hand.