Intital velocity v(0)= 5

initial position s(0) =3

a) fin velocity of particle at time t

v(t) = sin(t)+3t+C

plugging 0 for t I get C = 5

s(t) = -cos(t) + 3/2t^2 + 5t + C

plugging 0 for s I get C = 3

answer: v(t) = sin(t)+3t+5

b) What is the total distance traveled from t = pi to t = 2pi

integral pi to 2pi = v(t) = sin(t)+3t+5

= s(2pi)-s(pi)

Thanks!