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Riemann integrable functions

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Let f be a real function on [a, b]. Suppose that f is Riemann integrable on
[c, b] for every a < c < b.

(a) Show that if f is also Riemann-integrable on
[a, b] then integral b-a(f dx) = limc-a integral b-c(f dx).

(b) Give an example of a function g on [a, b] for which limc-a integral b-c(g dx) is defined, while g is not Riemann integrable on [a, b].

Please look in attachement for problems with correct symbols.

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Solution Summary

We prove properties using Riemann's definition for the integral.

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