Answer
\[
s(t)=1+t-\frac{2 t^{3}}{3}+\frac{t^{4}}{4}
\]
Work Step by Step
The position function is an integral part of the velocity function
\[
s(t)=\int v(t) d t=t-\frac{2 t^{3}}{3} +\frac{t^{4}}{4}+C
\]
\[
s(0)=1=C
\]
Determine $C$ using $s(0)=1$
\[
s(t)=1+t-\frac{2 t^{3}}{3}+\frac{t^{4}}{4}
\]
