1. The problem statement, all variables and given/known data Why does [itex] \int_a^b \, y \; dx [/itex] become [itex] \int_\alpha^\beta \, g(t) f^\prime(t) \; dt [/itex] if x = f(t) and y = g(t) and alpha <= t <= beta? 2. Relevant equations Substitution rule? 3. The attempt at a solution I'm not sure how y = y(x) in the integrand turns into g(t). Isn't y a function of x in the first expression? How do they go from y(x) to g(t)?