Hey, I just noticed:
you can take the derivative of an -affine- valued function
(b/c it's -differences-),
and you get a -vector- valued one;

Conversely, if you integrate a vector-valued function,
you still get a vector value out.

This is more deeply underlying why you lose the constant factor,
which is AKA the base point;

related points:
- derivative is invariant under translation
  ...which is basically saying "it's a property of underlying affine"
- derivative of any constant function is zero
  ...which also says "forget points"
