For the initial acceleration, the negative sign just indicates the direction of the acceleration, which depends on how you have defined your coordinate axis.

For the distance traveled in the 3rd second, you want to evaluate:

You should note that the velocity changes sign in this interval, so you want to find the root of the velocity function in this interval, and using the definition of absolute value, break this up into two integrals. Without the absolute value, what you are finding is the displacement, rather than the distance traveled, which is 1 meter.