Antiderivatives

(indefinite integrals)

Definition. Let the function , with an interval. is an antiderivative of if is differentiable on and

Written:

Properties of antiderivatives:

1. 
2. 
3. 

A function continuous on an interval has antiderivatives on that interval.

The derivative of any differentiable function on an interval has the Darboux property (the intermediate value property).

If has antiderivatives on the interval , then the function has the Darboux property on .