Let $a,b\in\mathbb{R}$ with $a<b$, and let $f:[a,b]\to\mathbb{R}$ be continuous on $[a,b]$ in the sense of \ref{def:continuity-closed-interval-c54-2026b}. Then $f$ is Riemann integrable on $[a,b]$ in the sense of \ref{def:riemann-integrable-closed-interval-c54-2026b}.