A rotor with rotational inertia \(I\) is mounted on a frictionless axle and is initially at rest. Starting at time \(t = 0\), a net external torque given by \(\tau(t) = bt\) is applied to the rotor, where \(b\) is a positive constant. Which of the following expressions represents the total work done on the rotor by the torque from \(t = 0\) to \(t = T\)?