- interchanging the limits changes the sign of the integral.

- an integral can be factorised with a constant.

- if the limits are the same, the integral is zero.

- the integral of the sum of two functions is the sum of the integrals.

- integrating a constant results in the constantbeing multiplied by the length of integration

- if the function is odd.

- if the function is even.

- the limits follow in a natural way.

For allandthenfor all

All the above integrals are examples of definite integrals – having limitsandIf an integral has no limits it is called an indefinite integral and to the integral of the functionwhich is writtenwe must add an arbitrary constant, usually written