Answer
Please see the work below.
Work Step by Step
We know that
$v=\int_0^t a dt$
$v=\int_0^t(a_{\circ}+bt)dt$
$v=v_{\circ}+a_{\circ}t+(\frac{b}{2})t^2$
(b) $x=\int _0^t v dt$
$x=\int _0^t (v_{\circ}+a_{\circ}t+\frac{b}{2}t^2)dt$
$x=x_{\circ}+v_{\circ}t+(\frac{a_{\circ}}{2})t^2+(\frac{b}{6})t^3$
