Definition:Adaptive Quadrature

Definition
Adaptive quadrature is a numerical integration algorithm for evaluating definite integrals of an integrand $f$ where the points at which $f$ are evaluated are chosen adaptively.

Hence if $f$ changes rapidly around a point $x$ in the interval of integration, the algorithm chooses small subintervals near $x$.

However, if $f$ changes slowly, the algorithm chooses larger subintervals near $x$.