Let and be two antiderivatives of the same function on an interval

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

F(x)

and

G(x)

be two antiderivatives of the same function

f(x)

on an interval

I

. Prove that

F(x)-G(x)

is a constant on

I

. Hence explain why the symbol ``

+C

'' is attached to every indefinite integral.