Question: (a) Prove that if g(x) := 0 for 0 < x < 1/2 and g(x) := 1 for 1/2 < x < 1, then the

(a) Prove that if g(x) := 0 for 0 < x < 1/2 and g(x) := 1 for 1/2 < x < 1, then the Darboux integral of g on [0, 1] is equal to 1/2.
(b) Does the conclusion hold if we change the value of g at the point 1/2 to 13?

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