Calculus has two moves. Differentiation reads off the slope of a curve at a point; integration adds up the area beneath it. They look unrelated — one is local and steep, the other is global and flat — until you notice this: the rate at which the area grows is exactly the height of the curve. Slide the point and watch the top curve's height become the bottom curve's slope.
Drag left–right anywhere on the plot to move the point c.
f(x) — the function (top)A(x) = ∫₀ˣ f — area so far (bottom)That equality is the Fundamental Theorem of Calculus: if A(x) = ∫₀ˣ f(t) dt is the running area, then A′(x) = f(x). Differentiation and integration are inverse operations — undo one with the other. It's why every area problem becomes "find an antiderivative": to get the area under f, find a function whose slope is f. Watch the bottom curve — where f is positive the area climbs, where f dips below zero the area falls (signed area), and where f crosses zero the area curve is momentarily flat, because a zero height means zero rate of change. The two halves of calculus were never separate; they're one relationship read in two directions.