What is the “t” value in a Gaussian CDF, and how do I calculate it?

Question

I was reading up on the formula for a Gaussian CDF:

$\Phi(x) = \frac12 [1 + $erf$(\frac{x}{\sqrt{2}})]$

where erf(x) is defined as:

erf$(x) = \frac{2}{\sqrt{\pi}} $$\int_0^x e^{-t^2} \,dt$

My question is, what is the $t$ variable in the formula, and how do I calculate it?

Thanks to anyone that can offer some help.