Editing Openai/690f817c-4724-800b-a047-fe00351b6d9c (section)

=== 2. Integrals are the reverse idea ===

If a derivative tells you the rate of change, an integral tells you the total accumulation of that change.
It’s like asking:

<blockquote>“If I know the speed of a car at every moment, how far did it travel overall?”</blockquote>

That total distance comes from adding up all the little bits of movement — each tiny piece of distance = speed × a tiny bit of time.

Mathematically, that “adding up” process is the integral.

So the integral of f(x)f(x)f(x) gives you the total area under its curve — or the accumulated value of f(x)f(x)f(x) — across some interval.