Give an example to show that integrability is not preserved by composition; that is, give an example of two bounded real-valued functions f on an interval [a, b] ⊂ R and g on an interval [c, d] ⊂ R containing f([a, b]) such that $\int_a^bf$ and $\int_c^dg$ exists $\int _a^bg ◦ f$ does not.
I thought about Riemann function, Dirichlet function and topologist's sine function but none of these works..
Could you please think of any?
