Looks like the repeating unit is -(Acr)p-(PLA)x-(PEG)m-(PLA)x-.
Yes, the integral ratios should work and it should be possible to determine for example <p/x>
or <p/m>
. After all the peaks are assigned :).
How broad are the lines? Is it possible that you see three peaks because there should be a multiplet?
Also, is it possible that certain conformation forces the protons in CH2 group become non-equivalent?
Finally I thought that in the cases where p=1 and p!=1 chemical shifts of acrylic residue will probably be different, no?
For the experiment to give correct integral ratios it's important to make sure that none of the resonances are even partially saturated. That can be achieved by using small flip angle for the pulse - maybe 20 degrees and allow sufficient relaxation (5*T1 is a good choice).choice). Figure 4.3 on p. 113 of Timothy Claridge "High Resolution NMR Techniques in Organic Chemistry" had a good illustration of that.
Being careful with the choice of recycling delay and pulse width will be especially important if spins of nuclei "whose" peaks the need to be integrated have substantially different T1 relaxation times, e.g. methyl vs methyne.
If the lines are wide and overlapping, line fitting may be required (for example in Origin or Matlab) to extract the integrals. Also - with lorentzian lineshapes integral reset points must be quite far from the peak because of the wide tails of the Lorentzian.