Show that composition of two Riemann integrable functions is not necessarily Riemann integrable.?

Answer 1

Define f(x)=1/x^2 for x<>0, =0 for x=0. Then int(f(x),x=1..infinity)=1, but since f(f(x))=x^4, the composition of f with itself is not Riemann integrable over [1,infinity).