Theorem 6-4 (Riemann Condition for Integrability): A bounded func- tion f defined on [a, b] is Riemann integrable on [a, b] if and only if, given € > 0, there is a partition P(s) of [a, b] such that S(f; P(8)) - S(f; P(€)) < €. Theorem 6-4 (Riemann Condition for Integrability): A bounded func- tion f defined on [a, b] is Riemann integrable on [a, b] if and only if, given € > 0, there is a partition P(s) of [a, b] such that S(f; P(8)) - S(f; P(€)) < €. 2. (a) Let f : (1,5] → R defined by 2 if x #3 f(x) = 4 if x = 3. Use Theorem 6-4 to show that f is Riemann integrable on (1,5). Find si f(x) dt. (b) Give an example of a function which is not Riemann integrable. Explain all details.