> [!note] Theorem > > If a [[Science/Math/Functions/Function|function]] $f$ is [[Continuity|continuous]] over a closed interval $[a, b]$, or if $f$ only has a finite number of *jump discontinuities*, then $f$ is integrable over $[a, b]$; that is, the [[Definite Integral|definite integral]] $\int_{a}^{b}f(x)dx$ exists.