$(1$ point$)$ Find the line integral with respect to arc length ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(7x+4y)ds,$ where $C$ is the line segment in the $xy-$plane with endpoints $P=(2,0)$ and $Q=(0,5)$

$($a$)$ Find a vector parametric equation vec$(r)(t)$ for the line segment $C$ so that points $P$ and $Q$ correspond to $t=0$ and $t=1,$ respectively.

vec$(r)(t)=$

$($b$)$ Using the parametrization in part $($a$),$ the line integral with respect to arc length is

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(7x+4y)ds={\displaystyle \underset{a}{\overset{b}{}}}$

$$ with limits of integration $a=$ and $b=$

$($c$)$ Evaluate the line integral with respect to arc length in part $($b$).$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(7x+4y)ds=$

$$