Definite integrals are used to find the exact value of the area under a curve between two points on the x-axis. It represents the accumulation of infinitesimally small areas and can be thought of as finding the total "signed" area.
Antiderivatives are functions that "undo" derivatives. They represent families of functions that have the same derivative.
Riemann Sums: Riemann sums are approximations of definite integrals by dividing an interval into smaller subintervals and summing up areas using rectangles or trapezoids.
The fundamental theorem of calculus establishes a connection between definite integrals and antiderivatives, stating that if F(x) is an antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a).