Introduction to Indefinite Integrals | Calculus Course: Theory Part 89

If you know a function's derivative, how much of the original function can you recover? This theory lesson is part of Calculus, Full Course with Theory and Practice. Explore antiderivatives, indefinite integrals, families of functions and the constant of integration through precise definitions and linked animated graphs. Understand why intervals matter, when antiderivatives exist, and how an initial condition selects one function. Assumed background: functions, coordinates and elementary derivative rules. Chapters 00:00 Antiderivatives and derivative graphs 02:05 Verification by differentiation 04:26 Families and constants on an interval 06:50 Indefinite integral notation 09:11 Antiderivative theorems and existence 11:06 Initial conditions