Basic Analysis I — Real Analysis · Problem 5.2.8

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · additivity-of-integral

Problem

Let f∈R([a,b])f \in \mathcal{R}([a,b]). Let α,β,γ\alpha, \beta, \gamma be arbitrary numbers in [a,b][a,b] (not necessarily ordered in any way). Prove ∫αγf=∫αβf+∫βγf.\int_\alpha^\gamma f = \int_\alpha^\beta f + \int_\beta^\gamma f. Recall what ∫abf\int_a^b f means if b≤ab \leq a.

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