As in the analogue computer world, the Integrator is the core workhorse of ACE.
At its most basic, it outputs a rising or falling slope signal based on the value and polarity of the input voltage. However, its uses in the synth world are as varied and wonderful as those in maths, science and engineering.
It is very simple to set up a sawtooth / ramp wave LFO / VCO using a single Integrator to retrigger itself. You can also chain two Integrators in a feedback loop to create a sine wave "harmonic oscillator". This can be linear frequency-modulated in both positive and negative directions, making it a true thru-zero oscillator ("zeroscillator"). Or turn up the Damping Factor and turn a harmonic oscillator into a 'pinged' percussion oscillator.