A particle moves along the x-axis with velocity given by v(t)=4t-20sin(t^2+1) for t>0. If the particles is at position x=pi at time t=0, which of the following gives the position of the particle at time t=4?

a. ∫4-0 (4t-20sin(t^2-1))dt
b.pi+∫4-0(4t-20sin(t^2-1))dt
c. d/dt(4t-20sin(t^2+1)) at t = 4
d. ∫4-0 |4t-20(t^2+1)|dt