3 questions:

1) let f: (a,b) -> (c,d) be continuos surjective monotonic function. prove f is invertible and its inverse is continuous

2) f: [0,1] -> R

f(x) = 0 if x is irrational;

f(x) = 1/n if x is rational with x = m/n and gcd(m,n) = 1

prove that f is riemann integrable and its integral from 0 to 1 is 0

3) let f(x) < g(x) < h(x) for all x in [a,b]

suppose f and h are riemann intagrable and integral of f from 0 to 1 equals integral of h from 0 to 1

prove g is riemann intagrable and integral of g from 0 to 1 equals integral of f from 0 to 1