### 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.

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