The angular frequency (ω) is almost constant. Therefore its integration will yield the output that will be a ramp, evantually causing the the output to be keep on rising. This is indeed true!
However, since the output represents an "angle" value, multiples of (2π) (such as (0, 2π, 4π...) correspond to the same angle. Therefore, resetting the integrator to 0 after reaching (2\pi) is not a "temporary" solution, but rather the correct approach. It is known as the "Integrator Wrap-up State."
Simulink provides an "Integrator with Wrapped State" block that offers this feature.
For further clarification, please refer to the MATLAB documentation here:
The documentation also recommends "wrapping the state" to obtain the angle.
I hope this clarifies any doubts you may have
