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Is this true?

A composition of Riemann integrable functions is Riemann integrable

No — it is false.

The counterexample

This one comes with the Notes pack.

See pricing

85 counterexamples are free — including most of the ones Part C leans on hardest.

The kind of mistake this is

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Watch it happen

Riemann sums closing on the integral

integration

Others that fail the same way

From Integration › Riemann integration and criteria

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