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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