Ok, digging up some books and my recent ATPL notes.
A rate gyroscope is used to detect rates of turn. It has only one gimbal ring and it has a calibrated spring connected between the gimbal ring and casing to restrain movement about the longitudinal axis. Pallet, Aircraft Systems and Integrated Systems
A rate integrating gyro can be found in an INS/IRS (usually a rate sensor - ie a RLG). An integrating gyro senses movement about one axis and that the rate changes are integrated to give distance changes.
A rate integrating gyro is also used in the stability or inner loop of the autopilot.
Pallet, own study notes
The intertial attitude indicator I am not too sure on but the stabilizing servo mechanism is found on the autopilot.
So, if was me, I would say the rate integrating gyro can be found on 1-4, the rate gyro, 5 only.
Good luck.