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How is absement related to position (displacement)?
More generally, how is integral related to derivative?

Absement changes as an object remains displaced and stays constant as the object resides at the initial position. It is the first time-integral of the displacement (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement.

What are integrals with respect to time?

The integral of acceleration with respect to time is velocity. The integral of velocity with respect to time is position. The integral of position with respect to time is absement.

Spacetime is not a geometric model only in terms of space. It is also temporal. Its geometry equally extends in terms of time.

The dimensions of time absolutely complement the dimensions of space.