Answer
\[
-2-t-\cos 2 t=s(t)
\]
Work Step by Step
The velocity function is an integral part of the acceleration function
\[
v(t)=\int a(t) d t=2 \sin 2 t+C
\]
\[
v(0)=-1=C
\]
Determine $C$ using $v(0)=-1$
\[
-1+2 \sin 2 t=v(t)
\]
Conclusion
\[
s(t)=\int v(t) d t=-t-\cos 2 t+C
\]
The position function is an integral part of the velocity function
\[
s(0)=-1+C=-3 \Rightarrow -2=C
\]
Determine $C$ using $s(0)=-3$
\[
-2-t-\cos 2 t=s(t)
\]
