integrating amplifier anyone?

hello there
big help is needed here pls pretty pls!
my easy (well,am a bit confused here) question wud be

what does an integrating amplifier do in real life?
i mean what is the application in any electronic devices when it comes to daily life facility?

ur help is much much appreaciated.thanks

Simple example for sound.
Average the incoming audio and output a steady volume voltage level. RMS measuring of the audio level is even possible, though complex.

An integrator makes perfectly linear ramps when the input is a square-wave.
An integrator makes a triangle-wave as part of a Pulse-Width-Modulation circuit for an efficient DC light dimmer or DC motor speed controller.
An integrator is a single order lowpass filter.

Here is an integrator that slowly increases the brightness then slowly decreases the brightness of an LED: