Answer the following sentences true or false and explain your answer in as much detail as possible: 1) The Reinmann–Stieltjes integral generalizes the Riemann integral 2) If f(x) is a function that is Riemann-Stieltjes integrable with respect to another function g(x), then f(x) is also Riemann integrable. 3) If g(x) is a function of bounded variation then every continuous function f(x) is Riemann-Stieltjes integrable with respect to g(x). 4) If f(x) is Riemann-Stieltjes integrable with respect to g(x) then g(x) is Riemann-Stieltjes integrable with respect to f(x). 5) Every continuous function is Riemann-Stieltjes integrable with respect to any function g(x).

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