Owl: You stroll east along a pier for three minutes at 2 m/s, then west for two minutes at 1.5 m/s. Your fitness watch reports how far your feet traveled. Your friend asks where you are relative to the start.
Those are different questions. One cares about total path length; the other about net displacement — and velocity's sign matters.
Integrating velocity gives net change of position. Integrating speed (absolute velocity) gives distance walked.
Before formulas: in your pier walk, is displacement equal to distance? Why or why not?