#### Answer

$4\sqrt(5)$

#### Work Step by Step

$y=2x-5$
$x=[-1,3]$
Equation y and its parameters are defined here
y'=2dx
Take the derivative of the equation given
$L=\int_{-1}^{3}\sqrt (1+(f'(x))^{2})dx$
Plug the upper and lower limits into to equation for arc length
$L=\int_{-1}^{3}\sqrt(1+(2)^2) dx$
Plug in the derivative of the original equation for f'(x)
$L=\int_{-1}^{3}\sqrt(5) dx$
$L=\sqrt(5)x|_{-1}^{3}$
Plug in upper and lower bounds
$L=3\sqrt(5)-(-\sqrt(5))$
Simplify
$L=4\sqrt(5)$