This paper presents PID tuning rules for first-order plus integrator systems. These tuning rules are derived by optimizing the integrated absolute errors of set point and load disturbance responses under robustness and bandwidth constrains. For deriving the tuning formulas, PID controllers for some normalized systems were designed. The relationship between the controller parameters, the parameters that characterize the system dynamics and the normalized gain crossover frequency are determined and the tuning formulas are then derived. Experimental results are provided to demonstrate the effectiveness of these tuning rules.