Exercise 4: (Hard) Give an example of a function f with domain [0, 1] with infinitely many points of discon- tinuity such that f is integrable from 0 to Hint: f can be discontinuous on the set {n-1, n e N}. Remark: There is no need to formally prove that f is integrable, a good explanation is fine.

Q: interval [a,b] where it is NOT integrable. f(x)=           ,   x∈

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Q: f is Riemann integrable iff f is bounded and f has finite set of discontinuous points.

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A: let f be Riemann integral an [a, b] then clearly f is bounded.