Double integration of raw acceleration data is a pretty poor estimate for displacement. The reason is that at each integration, you are compounding the noise in the data.
If you are dead set on working in the time-domain, the best results come from the following steps.
1. Remove the mean from your sample (now have zero-mean sample)
2. Integrate once to get velocity using some rule (trapezoidal, etc.)
3. Remove the mean from the velocity
4. Integrate again to get displacement.
5. Remove the mean. Note, if you plot this, you will see drift over time.
6. To eliminate (some to most) of the drift (trend), use a least squares fit (high degree depending on data) to determine polynomial coefficients.
7. Remove the least squares polynomial function from your data.
A much better way to get displacement from acceleration data is to work in the frequency domain. To do this, follow these steps...
1. Remove the mean from the accel. data
2. Take the Fourier transform (FFT) of the accel. data.
3. Convert the transformed accel. data to displacement data by dividing each element by -omega^2, where omega is the frequency band.
4. Now take the inverse FFT to get back to the time-domain and scale your result.
This will give you a much better estimate of displacement. Hope this helps..