Limits of sums and signed accumulation

Introduce definite integrals as limits of Riemann sums and as signed accumulation. Build right-endpoint sums on shifted intervals, evaluate simple limits with supplied finite-sum identities, and use geometry to separate net area from total geometric area. Single-select and multiselect questions include motion and flow interpretations, with worked explanations and careful sign checks. No antiderivative techniques or full integration-rule syllabus is needed. This optional bridge follows finite Riemann sums and emphasizes what an accumulated quantity means.