Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 273: 97

$s=t+\sin t+4$

We need to find the anti-derivative for $\dfrac{ds}{dx}=1+\cos t$ Thus, we have $s=t+\sin t+C$ Apply the initial condition $s(0)=4$ in the above equation to solve for $C$. we get: $4=0+\sin 0+C \implies C=4$ Hence, $s=t+\sin t+4$