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?