Answer the following True or False.

If g(x)\displaystyle {g{{\left({x}\right)}}} is a continuous function and h(x)\displaystyle {h}{\left({x}\right)}  is differentiable such that h(a)=h(b)\displaystyle {h}{\left({a}\right)}={h}{\left({b}\right)} , then

 abg(h(x))h(x)dx=0\displaystyle {\int_{{a}}^{{b}}}{g{{\left({h}{\left({x}\right)}\right)}}}{h}'{\left({x}\right)}{\left.{d}{x}\right.}={0}.