First integrate the entire spectrum and set the value equal to the total number of protons, 18 for this sample.
Next create subintegrals for each of the peaks
It will probably be apparent at this point, that the integration values are not quite right. Many of the values will be fractions, possibly far from whole numbers. This zoom view of integration results from 0.8 to 2.5 ppm shows the problem.
Now improve the values for the integration by picking a peak with a known value, methyl groups are usually easy to spot at the right (small chemical shift) end of the spectrum. The rough integration values should help you decide if a peak is from one or more methyl groups (ie: 3, 6, or 9 protons). Set the value for this peak, and see how the remaining integration values look. The spectrum below shows the results after the integration value for doublet at 0.9 ppm to set to 3. Notice that values are much closer to integers
Full Spectrum with new integration.
This integration data does not quite fit. It may be useful to go back and improve the baseline correction of the FID prior to the transform, or work on the baseline for the spectrum. Also, don't expect very good integration of broad peaks and multiplets. If the integration is still not satisfactory, you may need to reaquire the spectrum. For the best integration; average a large number of pulses, use 90 degree pulses, wait 5 T1's between pulses.