This blocks computes y as integral of the input u multiplied with the gain k. If the integral reaches a given upper or lower limit and the input will drive the integral outside of this bound, the integration is halted and only restarted if the input drives the integral away from the bounds.
It might be difficult to initialize the integrator in steady state. This is discussed in the description of package Continuous.
If parameter limitsAtInit = false, the limits of the integrator are removed from the initialization problem which leads to a much simpler equation system. After initialization has been performed, it is checked via an assert whether the output is in the defined limits. For backward compatibility reasons limitsAtInit = true. In most cases it is best to use limitsAtInit = false.
If the reset port is enabled, then the output y is reset to set or to y_start (if the set port is not enabled), whenever the reset port has a rising edge.