#### Answer

$2$

#### Work Step by Step

The formula to calculate the arc length is as follows: $L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$
Re-write the equation as follows:
$L=\int_{-\pi/4}^{\pi/4} \sec^2 y dy $
Separate the terms and integrate as follows:
$L=[ \tan y]_{-\pi/4}^{\pi/4} \\= (\tan \dfrac{\pi}{4} -\tan \dfrac{-\pi}{4} ) \\= 2$