$(4)(5pts)$ A dog $is$ running towards a ball. Her position $at2$ seconds $is$ known $tobe5$

meters from her starting position; that $is,s(2)=5.$ Her velocity $is$ given $by$ the function

$v(t)=2t+4t^3,in$ meters per second, and the time $tis$ given $in$ seconds. Find the position

function $s(t).$ Simplify $so$ that your final answer does not contain $an$ integral.