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How to prove from first principles that a function is Riemann integrable

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Quick description

This article is about how to prove that a function is Riemann integrable if for some reason you need to do so directly from the definition.

Prerequisites

Basic undergraduate real analysis.

Example 1

If and are both Riemann integrable functions defined on , then so is , and .

Example 2

Every monotone function defined on the closed interval is Riemann integrable.

Example 3

Every continuous function on the closed interval is Riemann integrable.