The acceleration of an object is given by the function a(t) = -t/2 + 9/4. Also at time t=0, the velocity of the object is -2. Find the difference between the distance and the displacement traveled by the object to the nearest integer from t=0 to t=10.

Okay so this is what i have so far...

I took the integral of the acceleration to get the velocity and what I obtained was 9t/4 - (t^2)/4 + C

then I got -2 = C

I then integrated the velocity equation to get the position equation and I got -(t^3)/12 + (9t^2)/8 -2t + C.

How do I find C for the position equation?

Or did I go to far...

I know I need to set an equation equal to zero to determine min and max to see where the function changes direction and then I set up an integral of the same function from 0 to one point then from that point to 10...

can someone please help me?