- #1

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## Main Question or Discussion Point

Assume that a function [itex]f:[a,b]\to\mathbb{R}[/itex] is differentiable in all points of its domain, and that the derivative [itex]f':[a,b]\to\mathbb{R}[/itex] is bounded. Is the derivative necessarily Riemann integrable?

This what I know:

Fact 1: Assume that a function is differentiable at all points of its domain. Then the derivative is not necessarily Riemann integrable.

Fact 2: Assume that a function is bounded. Then the function is not necessarily Riemann integrable.

So my question is not obvious.

This what I know:

Fact 1: Assume that a function is differentiable at all points of its domain. Then the derivative is not necessarily Riemann integrable.

Fact 2: Assume that a function is bounded. Then the function is not necessarily Riemann integrable.

So my question is not obvious.

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