Moderate# Total Distance Of A Particle

APCALC-LYHI08

A particle in the $xy$-plane moves according to the following equations: $x(t)=\cfrac {1}{2} \cdot t^2+t + 4$ and $y(t)=\cfrac {3}{2} \cdot t^2-2t -8.$

Find the correct expression for the total distance the particle has traveled from time $t = 1$ to $5$.