In this paper, a bounded integral controller (BIC) is proposed for regulating non-linear systems with guaranteed closed-loop system stability. It is proven that the BIC generates a bounded control output independently from the plant parameters and states and guarantees closed-loop system stability in the sense of boundedness with the only knowledge of the input-to-state (practical) stability (ISpS) of the plant. Furthermore, an analytic selection of the BIC parameters is presented to guarantee a given bound for the control output, suitably extending the BIC application to locally ISpS plant systems as well. Its performance is investigated using non-linear Lyapunov methods and it is proven that it can approximate the behavior of the traditional integral controller (IC) near steady state. Simulation results of a locally ISS system are provided to compare the BIC with the IC operation under a given bound of the control output.