Let f : [a,b] → R be a Riemann integrable function. Let α > 0 and β ∈ R. Then define g(x) := f(αx+β) on the interval I = [1/α(a−β), 1/α(b−β)]. Show that g is Riemann integrable on I
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f(x) = {2 if x ! [0, 1) −1 if x = 1 3 if x ! (1, 2] −5 if x ! (2, 3) 20 if x = 3 } Prove that the function is Riemann
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