Indefinite integrals and antiderivatives

An introduction to the notion of an "indefinite integral", its close connection to the idea of an antiderivative, and its role (via the Fundamental Theorem of Calculus) as an "incipient" or "potential" definite integral. The video ends with the subtle example of ∫ 1/x dx: what is the most general antiderivative of the reciprocal function? Generally, when the domain of the integrand consists of disconnected subintervals, then an independent constant of integration may be assigned for each subinterval.

[ezrasteinberg]

Wow! You are the first person to point out that with disconnected domains the arbitrary constant associated with a member of the family of antiderivatives can be different depending on which piece of the domain you are referring to. Excellent point! Thanks for passing along that important bit of information. :-)