Answer
\[
s(t)=7-3 t+t^{2}
\]
Work Step by Step
The position function is an integral of the velocity function
\[
s(t)=\int v(t) d t=-3 t+t^{2}+C
\]
Determine $C$ using $s(1)=5$
\[
s(1)=-3+1+C=5 \Rightarrow C=7
\]
Conclusion
\[
7-3 t+t^{2}=s(t)
\]
