Last year just for the fun of it, we have written a TrcGyro class subclassing the WPILib gyro so that we can add GetAngularVelocity and GetAngularAcceleration, not that we really need them. Strange that the WPILib used the accumulater to integrate for the angular displacement but never give you the raw angular velocity. So I wrote the class to differentiate the angular displacement to get back angular velocity. If you take this code, change the differentiator to integrator, create a member variable to remember the previous angular velocity and change the algorithm from dividing to multiplying, then you have an integrator.
http://proj.titanrobotics.net/hg/Frc...clib/TrcGyro.h
If you really want to see how to do the integration, we have written a gyro module for the FTC using RobotC. Look at the GyroTask function. You can find it here. As a bonus, this code does gyro calibration to determine the bias as well as the noise level.
http://proj.titanrobotics.net/hg/Frc...lib.nxt/gyro.h