$\displaystyle L = \int^{2\pi}_{0}\sqrt{(-sin t)^2 + (cos t)^2 + (\frac{1}{\pi})^2} dt $

$\displaystyle = \int^{2\pi}_{0}\sqrt{sin^2t+cos^2t+(\frac{1}{\pi^2 })} dt $

this is an example from the book it skipped a step, i dont know how they got the next step:

$\displaystyle = \int^{2\pi}_{0}\sqrt{1+\frac{1}{\pi^2}}dt $

$\displaystyle = 2\pi\sqrt{1+\frac{1}{\pi^2}} $ is the arc length