Problem $1(50$ points$).$ For the beam shown below with a constant $El,$ answer the questions with the given $x-$axis using Integration Method:

$($a$)[10$ points$]$ List four boundary conditions of the beam.

$($b$)[10$ points$]$ Determine the equation of the distributed load, $(x).$

$($c$)[10$ points$]$ Determine the equation of the bending moment, $M(x).$

$($d$)$ points$]$ Determine the equation of the elastic curve, $y(x).$

$($e$)$ points