Calculus I spent an entire course teaching you to go from a function to its derivative. This course spends its first real idea running that tape in reverse: given a rate of change, recover the quantity that produced it. That single reversal — "what function has THIS as its derivative?" — is the antiderivative, and it turns out to answer a question that looks, at first, nothing like a derivative at all: the exact area trapped under a curve.
Those two questions — undo a derivative, and measure an area exactly — seem unrelated until the Fundamental Theorem of Calculus, arguably the single most important result in this entire two-course sequence, proves they're the same question. This chapter doesn't get to the Fundamental Theorem's full statement or its name yet — that's next chapter's job — but it builds every tool the proof depends on: the derivative rules you're expected to run without thinking, the chain rule read backward as recognition instead of computation, the Riemann sum that defines area as a limit of rectangles in the first place, and u-substitution, the reverse chain rule's actual computational engine.
Two threads of review are woven in on purpose, not bolted on as an afterthought. The algebra survival kit — factoring, long division, completing the square — resurfaces here because integration, unlike differentiation, routinely REQUIRES you to reshape an expression before any rule applies; there's no integration analogue of "just apply the power rule term by term" that works on everything. And the trig identities, exponential/logarithm derivatives, and inverse trig derivatives get a dedicated pass because the rest of this course leans on being able to recognize their antiderivative forms on sight, the same way Calculus I needed the unit circle memorized cold.
The chapter closes with L'Hôpital's rule — technically a derivative tool, not an integration one, but the cleanest way to finish off the \frac{0}{0} and \frac{\infty}{\infty} limits that still show up constantly once functions get more complicated, and useful again much later when Taylor series need to compare growth rates. By the end of this chapter, nothing here is new — it's the derivative course you already took, sharpened into the specific toolkit integration is about to demand of it.