Suppose that a < b < c. Decide which of the following statements are true and which...

Suppose that a < b < c. Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples for the false ones.

a) If f is Riemann integrable on [a, b], then f is continuous on [a, b].

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b) If | f | is Riemann integrable on [a, b], then f is Riemann integrable on [a, b].

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c) For all bounded functions f : [a, b] → R,

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d) If f is continuous on [a, b) and on [b, c], then f is Riemann integrable on [a, c].