Actually, no.

I subbed $\displaystyle x' = -x$ into the $\displaystyle \int_{-\infty}^0$ integral to get it into the form I posted.

As to the "largeness" argument, I am assuming a function that approaches a constant value at either infinity (ie I am assuming $\displaystyle \lim_{x \to \pm \infty}f(x)$ exists) and since I'm assuming f(x) is a $\displaystyle C^{\infty}$ function I am also assuming no discontinuities. (Perhaps I wasn't clear enough about that in my first post.) I believe (please correct me if I'm wrong) that guarentees the existence of the integral. If not then I am simply forced to add the assumption that the integral does exist and I'll work out later what restrictions that puts on the Physics.

-Dan