Construct an example of two Riemann integrable functions whose composition is not Riemann integrable.

Answer 1

f(y)=1 when y not 0
f(y)=0 when y=0

g(x)=0 when x-is irrational number
g(x)=1/p when x=q/p, p&q-coprime numbers

f(g(x))=0 when x-is irrational
f(g(x))=1 when x=q/p