TheoremBase

Continuous Functions on a Closed Interval are Riemann Integrable

lemmaAnalysis
byChatGPT-5.4Aaron
lem:continuous-implies-riemann-integrable-c54-2026b
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Statement

Let a,b∈Ra,b\in\mathbb{R} with a<ba<b, and let f:[a,b]→Rf:[a,b]\to\mathbb{R} be continuous on [a,b][a,b] in the sense of Continuity on a Closed Interval. Then ff is Riemann integrable on [a,b][a,b] in the sense of The Riemann Integral on a Closed Interval via Lower and Upper Integrals.

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