Integration typically acts as a lowpass filter. For mechanical vibrations, you should make sure that your acquired signal is AC coupled or that you remove any DC component from the signal to integrate as this DC component will dominate the response and you will see a net displacement after integrating that isn't true of the real system.
You can integrate in the time-domain via filtering or numerical integration, or you can integrate in the frequency domain by simple scaling of the magnitude spectrum and shifting of the phase spectrum. It is easiest to integrate in the frequency domain because you don't have to worry about DC components dominating the velocity or displacement signals as it is easy to null the first bin in the spectrum. On the other hand, if you need the time-domain displacement, you will have to use a time-domain technique. If you use filtering, be sure to allow enough time for the filter to settle before doing any additional measurements. If you use a numerical integration technique, pay particular attention to the initial conditions you use. Good luck.
