The correct answer is C. The error signal is summed over a discrete time interval and accumulated by the controller.
The integral mode of a controller is used to eliminate steady-state error. It does this by integrating the error signal over time. This means that the integral mode will continue to add to the control signal as long as there is an error. This will eventually cause the error to reach zero, at which point the integral mode will stop adding to the control signal.
On a digital controller, the integral mode is implemented by summing the error signal over a discrete time interval. This means that the error signal is sampled at regular intervals and the values are then summed. The result of this is a cumulative error signal that is used to calculate the control signal.
The other options are incorrect. Option A is incorrect because digital controllers can handle integral mode. Option B is incorrect because the error is not divided into discrete amounts, it is summed. Option D is incorrect because not all of the above are correct. Option E is incorrect because the correct answer is C.