Definite integrals: ∫ₐᵇ f(x)dx = F(b) - F(a) where F is antiderivative. No +C needed (cancels). Geometric interpretation: Area between curve and x-axis from x=a to x=b. Properties: (1) ∫ₐᵃ f(x)dx = 0; (2) ∫ₐᵇ f(x)dx = -∫ᵇₐ f(x)dx; (3) ∫ₐᶜ f = ∫ₐᵇ f + ∫ᵇᶜ f; (4) ∫ₐᵇ [f+g] = ∫ₐᵇ f + ∫ₐᵇ g. Example: ∫₀² 3x² dx = [x³]₀² = 8 - 0 = 8. Solving: Find antiderivative; evaluate at limits; subtract. Exam tip: Be careful with limits. Include units for area problems. Understand negative area (curve below x-axis).