Find an antiderivative of f(x)=4x2. Give one without +C.
Riemann sumf(x) = 4x², n = 8
curve fexact area = 85.338 rectangles (right edge) = 102
Right-endpoint rule: each of the 8 rectangles is as tall as the curve at the right edge of its strip (width Δx = 0.5). That leaves a visible seam between rectangle top and curve: R₈ = 102 against the exact 85.33 — 16.67 too much. More strips shrink that seam to nothing — that passage to the limit is the integral.