text: ok...the integral of cos(t^2) is the right question...but its not the whole question? here's the whole question an object moving along a curve in the xy-plane has position (x(t),y(t)) at time t>0 with dx/dt=3+cos(t^2)  the derivative dy/dt is not given. at time t=2, the object is at position (1,8).  find the x-coordinate of the position of the object at t=4.   this is some pretty serious math... according to my calculation (hopefully it's right)  x(t) = (3.5t - 6) + 0.25 (sin2t - sin4),  so x(4) = 14 - 6 + 0.25 (sin 8 - sin 4) = 8.43654018548