The antiderivative

To compute a definite integral without really summing infinitely many little rectangles, the brilliant idea is to look for a function $F$ whose derivative is $f$: the antiderivative. The sum of the differentials $dF$ from $a$ to $b$ is nothing but the total increase of $F$, that is $F(b)-F(a)$. This link — the heart of the fundamental theorem of calculus — turns an integral into a subtraction.

• The antiderivative, inverse of the derivative
• Computing the area with the antiderivative