The drift is not evident in the first moments of functioning so it was satisfying enough for our purpose.
I tried anyway to correct it (to make the robot stand up hours and hours) using a band-pass filter (instead of an integrator) but it was not working as well as one would expect.
...Are you aware of any other method?
It would certainly be better not to have to integrate: this would avoid the integration drift.
As a conclusion... if you're thinking of creating your own Arduway think of replacing the gyroscope with a compass that directly returns the angle.