Integrators can be one type of Low Pass Filter. They are used by some ADC or in wave shaping.
An integrator circuit produces a steadily changing output voltage for a constant input voltage.
Similarly, the Differentiators are High Pass filters.
A differentiator circuit produces a constant output voltage for a steadily changing input voltage.
Adders are used by some temperature, pressure or some other parameter measuring device and getting their average. Mathematical circuits.
If the input resistances of a summing amplifier are connected to potentiometers the individual input signals can be mixed together by varying amounts. For example, measuring temperature, you could add a negative offset voltage to make the display read "0" at the freezing point or produce an audio mixer for adding or mixing together individual waveforms (sounds) from different source channels (vocals, instruments, etc) before sending them combined to an audio amplifier.