Owl: Two city skyline silhouettes — an upper roofline u(x) and a lower roofline ℓ(x) — enclose a courtyard between their intersection points. Planners want the courtyard's area.
You don't integrate u alone or ℓ alone. You integrate the positive vertical gap u − ℓ, but only after you know which curve is on top on each stretch.
If the silhouettes cross, "upper" and "lower" can swap. Blindly writing ∫(f − g) without a sketch is how courtyard estimates go negative or nonsense.
How do you decide which region to add when two graphs cross?