In this paper, a laboratory experiment has been used to investigate some aspects related to integral action in model predictive control (MPC). Simulations using the same model as that used for control design may indicate that integral action is present and that disturbances are handled well with no steady-state offset, but in practice, unmodeled phenomena may give a poor response, including a steady-state offset. The reason is that the controller may not contain feedback with integral action, although the zero offset seems to indicate it. The experiments on a two-tank process verify that output feedback with input-disturbance estimation is efficient, provided that the disturbances to estimate are correctly chosen.