Which functions are Riemann integrable?

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In this lecture, we demonstrate that two classes of functions are integrable: continuous functions and increasing or decreasing functions on closed intervals [a, b]. By the way, you could extend the integrability of continuous functions to those that are continuous everywhere except a finite number of points.
  1. Josef Sifuentes
  2. Real Analysis
  3. Mathematics
  4. Riemann
  5. Integrability
  6. Integral
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I have some questions. @10:39 why it is L(f, P_k) instead of L(f, P_(k-1))? On the right hand side of the equation, it is the lower sum for partition P_(k-1).

tonyli