Doing the actual integration in the error-function.

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I got a question. The error-function is defined as:

$erfc(z)=\frac{2}{\sqrt{\pi}}\int_0^zdw\exp(-w^2)$.

How do I do the actual integration? I can't simply say that

$\frac{2}{\sqrt{\pi}}\int_0^zdw\exp(-w^2)=\frac{2}{\sqrt{\pi}}[-\frac{1}{2w}\exp(-w^2)]_0^z$, right? Because I can't evaluate it at w=0.

In my workbook there's a hint to look at it as a line integral, but I don't know how to approach it with that.

The general form of a line integral is $\int_\mathbb{C}f(z)dz=\int_a^bf(r(t))|r'(t)|dt$, but what would be my $r(t)$ in this case?

Any help would be appreciated.