question about integration of spectrum

hi all,
i want to get a integral spectrum, i have two choices:

1:do integration to time domain then do fft to get the spectrum
2:do integration to fft spectrum directly

i do not know which is better, can anyone give me some advices.

and if we do integration to a spectrum ( multiply 1/(j*w) ), how can we
deal with 0 Hz?




.

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