The principle of low-gain integral control for finite-dimensional systems is well known. More recently, low-gain integral control results have been obtained for classes of infinite-dimensional systems. In this paper we show that integral control with a simple and natural adaptation of the integrator gain achieves tracking of constant reference signals for every exponentially stable, multivariable, well-posed, infinite-dimensional, linear system whose steady-state gain matrix has its spectrum in the open right-half plane. Our results considerably extend, improve, and simplify previous work by the authors [SIAM J. Control Optim. 35 (1997), pp. 78-116].