Integral of a square root...

Problem which looks difficult but is indeed very easy.

The only root of polynomial is 1, whole function we are integrating can therefore be written as |x-1| (absolute value) and it is easy to integrate it on given integral.

$\displaystyle \int_{0}^{1}\sqrt{x^{2}-2x+1}dx$ $=\displaystyle \int_{0}^{1}\sqrt{(x-1)^{2}}dx$ $=\displaystyle \int_{0}^{1}|x-1|dx=\frac{1}{2}$