# Parametric arc length?

## I don't understand the part where the integral bounds switch to arctan. Why is this necessary? The red marks mean "1" since the bounds are $0 \setminus \le t \setminus \le 1$ (not $2 \setminus \pi$)

$\setminus {\int}_{0}^{\setminus} \textcolor{b l u e}{1} \setminus \sqrt{1 + \setminus \textcolor{red}{{t}^{2}}} \setminus \textcolor{o l i v e}{\mathrm{dt}}$
$\setminus {\int}_{0}^{\setminus} \arctan \left(\setminus \textcolor{b l u e}{1}\right) \setminus \sqrt{1 + \setminus \textcolor{red}{\setminus {\tan}^{2} \setminus \theta}} \setminus \textcolor{o l i v e}{\setminus {\sec}^{2} \setminus \theta d \setminus \theta}$