Why can the error function be written in two ways?

Question

I have read that the error function can be written as

$$erf(x) = \dfrac{2}{\sqrt{\pi}}\cdot\int_{0}^{x}{e^{-t^2}}~\mathrm{d}t$$

and

$$erf(x) = \dfrac{1}{\sqrt{\pi}}\cdot\int_{-x}^{x}{e^{-t^2}}~\mathrm{d}t$$

and they mean the same thing. What is the reason for this?

Answer 1

It should be obvious that the shaded area on the left is half the shaded area on the right: