Question: Suppose that f' exists and is integrable on [a ,b]. Prove that f is of bounded variation and If f' is bounded rather than integrable,

Suppose that f' exists and is integrable on [a ,b]. Prove that f is of bounded variation and

Suppose that f' exists and is integrable on [a ,b].

If f' is bounded rather than integrable, how do the upper and lower integrals of f' compare to the variation of f?

Var(f)- | lf,(x)I dx

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