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## Homework Statement

Lets say we have the velocity equation for a particle

v(t) = at^3 - bt^2 + ct^ - d with t between 0 and 5

So, to find its displacement I have to integrate v(t) from 0 to 5, and I understand why.

But if I want to find the total distance traveled, I must find where t is negative and then i integrate according to that. So, I would have something like an integral of v(t) from 0 to 4 minus an integral of v(t) from 4 to 5. But why do we subtract? Can anybody explain that to me? We also consider moving backwards when we calculate the total distance traveled right?

Thanks