Measure, Integration & Real Analysis · Problem 1A.5

Measures — Sheldon Axler

Mathematics — Measure Theory · riemann-integral-negation

Problem

Suppose f:[a,b]→Rf : [a, b] \to \mathbf{R} is Riemann integrable. Prove that the function −f-f is Riemann integrable on [a,b][a, b] and ∫ab(−f)=−∫abf.\int_a^b (-f) = -\int_a^b f.

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