An op-amp configured to integrate the signal that is coming in. As an integrator is the sum of the signal up to that point, an op-amp integrator will increase its output for positive input signals and decrease its output for negative input signals.
An op-amp integrator simulates mathematical integration, which is basically a summing process that determines the total area under the curve of a function.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd
An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Integration is an important part of many engineering and scientific applications. Mechanical integrators are the oldest application, and are still used in such as metering of water flow or electric power. Electronic analogue integrators are the basis of analog computers and charge amplifiers. Integration is also performed by digital computing algorithms.