Interval/Real function/Compact subintervals/Riemann integrable/Definition

Riemann-integrable function

Let ${}f\colon I\rightarrow \mathbb {R}$ be a function on a real interval. Then ${}f$ is called Riemann-integrable, if the restriction of ${}f$ to every compact interval ${}[a,b]\subseteq I$ is Riemann-integrable.