The Fundamental Theorem of Calculus is the bridge between differentiation and integration: they are inverse operations. This guide covers FTC Part 1 (the derivative of an accumulation function is the integrand), FTC Part 2 (evaluating a definite integral as F(b) − F(a) for any antiderivative), the geometric intuition behind why the theorem works, a step-by-step procedure for evaluating definite integrals (including u-substitution), common mistakes — applying FTC across a discontinuity, sign errors, confusing definite and indefinite notation — and worked examples covering polynomials, trig, chain-rule FTC1 problems, net displacement vs total distance, average value, and physics applications.