The total charge that flows due to a flux change: $Q = \int I\,dt = \int \frac{\varepsilon}{R}\,dt = \frac{1}{R}\int \frac{d\Phi}{dt}\,dt = \frac{\Delta\Phi}{R} = \frac{N(\Phi_1 - \Phi_2)}{R}$. The charge depends only on the total flux change, NOT on how quickly the change occurs. A fast change gives large current for a short time; a slow change gives small current for a long time — but the total charge is the same. This principle is used in ballistic galvanometers.