Continuous functions are Riemann integrable - Imported Knowlpedia Content

Continuous functions are Riemann integrable: If $f:[a,b]\to\mathbb{R}$ is continuous, then $f$ is Riemann integrable on $[a,b]$ .

Remarks

This theorem guarantees that the Riemann integral covers all standard functions from calculus and is a basic entry point for more refined integrability criteria.