Proof

.

2. If the function is integrable on the intervals joining , then

.

This property can be simply proved by using geometrical meaning of the definite integral.

3. The integral of times the function is times the integral of the function

.

Proof. - antiderivativeof the ;

- antiderivative of the

4. The integral of the constant function over an interval is the product of the length of the interval and the constant

.

5. The integral of the algebraic sum of the functions is equal to the sum of its integrals.

Proof. - antiderivative of the ;

- antiderivative of the ;

- antiderivative of the , than

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