From Wikipedia (PID Controller), which helps to explain why you get O2 sensor cross counts - maybe?
Integral
An
integral term increases action in relation not only to the error but also the time for which it has persisted. So, if the applied force is not enough to bring the error to zero, this force will be increased as time passes. A pure "I" controller could bring the error to zero, but it would be both slow reacting at the start (because the action would be small at the beginning, depending on time to get significant) and brutal at the end (the action increases as long as the error is positive, even if the error has started to approach zero).
Applying too much integral when the error is small and decreasing will lead to overshoot. After overshooting, if the controller were to apply a large correction in the opposite direction and repeatedly overshoot the desired position, the output would
oscillate around the setpoint in either a constant, growing, or decaying
sinusoid. If the amplitude of the oscillations increases with time, the system is unstable. If they decrease, the system is stable. If the oscillations remain at a constant magnitude, the system is
marginally stable.