The error function is definted as $erf(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-p^2} dp$. I have the function $\frac{2}{\sqrt{\pi}}\int_{-\infty}^0 e^{-p^2}dp$. I can switch the bounds of the integral, then I would have $-\frac{2}{\sqrt{\pi}} \int_0^{-\infty} e^{-p^2} dp$. However, if I switch the signs of the limits then I have a different expression that I am taking the integral of and hence I don't have the error function anymore. I do believe the answer is one, just like $\frac{2}{\sqrt{\pi}} \int_0^{\infty} e^{-p^2} dp = 1$. This is for a partial differential equations class.
Side note: This should probably belong in META, but how do we search very specific questions on this website? Sometimes I post a question and there is a link that someone posts that goes to a question very similar to mine (which I can use to solve the problem). But whenever I search myself I can never find anything. Not sure if it has to be typed in LaTeX.
$$\frac{2}{\sqrt{\pi}}\int_{-\infty}^0 e^{-p^2}dp=-\frac{2}{\sqrt{\pi}}\int_{0}^{-\infty}e^{-p^2}dp=-\lim_{x\rightarrow-\infty}\text{erf}(x) = \lim_{x\rightarrow\infty}\text{erf}(x)$$
The last step is because $\text{erf}(x)$ is an odd function. Credit to @march's comment for helping me spot that.
I also believe that the answer is $1$.
As for searching for specific questions, I would recommend checking out this thread. Personally when I search for questions, I avoid searching using any math expressions instead search for key words that might be related in both Google and Stack Exchange. In this case, I would have tried googling "alternate forms of the error function" or something like that.