Compact interval/Real function/Riemann integrable on partition/Fact/Proof/Exercise

Let ${}I=[a,b]$ be a compact interval. Prove that ${}f$ is Riemann-integrable if and only if there is a partition

${}a=a_{0}<a_{1}<\cdots <a_{n}=b\,$

such that the restrictions

${}f_{i}=f{|}_{[a_{i-1},a_{i}]}\,$

are Riemann-integrable.

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