We consider an output feedback control problem of a chain of integrators under sensor noise. The sensor noise enters the output feedback channel in an additive form. A similar problem has been addressed most recently in [9], but their result has been developed only under AC sensor noise. We generalize the result of [9] by allowing the sensor noise to include both AC and DC components. With our new output feedback controller, we show that the ultimate bounds of all states can be made arbitrarily small. We show the generality of our result over [9] via an example.