Suppose I have an integral
$$\int_{0}^{m}\dots dx$$
and I introduce a new variable $y = \frac{1}{x}$. Supposed that I can correctly treat the integrand, this yields
$$\int_{\infty}^{1/m}\dots dy$$
Now compare this with
$$\int_{-0}^{m}\dots dx$$
which leads to $$\int_{-\infty}^{1/m}\dots dy$$
Which one is valid and why?