True/false convergence of integral from 1 to infinity

[IntegrateMe]

Suppose h(x) is a continuous function for x > 0. If $$\int^∞_1{h(x)dx}$$ converges then for constant 0 < a < 1, $$\int^∞_1{h(\frac{x}{a})dx}$$ also converges.

The answer is true. Anyone care to explain why? I would have chosen false, because I was thinking that h(x/a) is larger than h(x) so we wouldn't know if it converges or not.

 

[tiny-tim]

hint: substitution