Integration of sqrt(1+t^2)dt

How can I integrate: $\displaystyle \int^1_{0}\sqrt{1+t^2}dt$?

The obvious choice seems like substitution, but I got a bit stuck doing it that way:

$\displaystyle u=1+t^2$

$\displaystyle \frac{du}{dt}=2t$

$\displaystyle du=2tdt$

If it were $\displaystyle du=2dt$, then I could just multiply the limits by 2, but since there is a $\displaystyle t$ in there too, I'm not sure what to do, since it leaves the expression still with the unknown, $\displaystyle t$, in there.

How can I do this?

Thanks