# Riemann integrable function

1. Let f: [a,b] ----> R and suppose f is integrable with respect to alpha. Prove that for any c in the real numbers, cf is integrable with respect to alpha and the integral from a to b of cf d(alpha) = c times integral from a to b of f d(alpha).

Give an example of a function f : [0,1] ----> R such that f is Riemann integrable and f is discontinuous on a dense subset of [0,1].

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Riemann integrable function is modeled.

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