Integrals
Integration undoes differentiation, and a definite integral gives the area under a curve.
A worked example
∫ 4x³ dx from 1 to 2: an antiderivative is x⁴, so the value is 16 − 1 = 15.
The mistake people actually make
An indefinite integral needs + C, because differentiating destroys constant terms. A definite integral does not.