(2) Let g [a, b] R be differentiable and assume g' is continuous. Let f [c, d] R be continuous and assume g([a, b]) = [c, d] so the composition f(g(x)) is well defined for each x = [a, b]. Prove the change-of-variables formula b Lisib g(b) | f(g(x))g'(x) dx = J f(x) dx. g(a) a