An improper integration fraction is reduced to a proper fraction by division.

Explanation:
An improper fraction is a fraction where the numerator is equal to or greater than the denominator. In the context of integration, an improper fraction refers to a fraction where the degree of the numerator polynomial is greater than or equal to the degree of the denominator polynomial.

To integrate an improper fraction, we need to perform polynomial long division. Polynomial long division is a method used to divide one polynomial by another polynomial of lower degree. It allows us to express the improper fraction as a sum of a polynomial and a proper fraction.

Here is the step-by-step process of reducing an improper integration fraction to a proper fraction:

1. Divide the numerator polynomial by the denominator polynomial using polynomial long division. This process involves dividing the highest degree term of the numerator by the highest degree term of the denominator and then multiplying the divisor by the quotient obtained.

2. Subtract the result obtained in the previous step from the numerator polynomial to obtain a new polynomial.

3. Repeat the division process with the new polynomial and the denominator polynomial until the degree of the new polynomial is lower than the degree of the denominator polynomial.

4. The final result of the division process is the sum of the quotients obtained at each step, which represents the polynomial part of the fraction, and a proper fraction obtained from the remainder.

5. Integrate the polynomial part of the fraction using the power rule for integration.

6. Integrate the proper fraction part of the fraction using standard integration techniques, such as substitution or partial fractions.

By following these steps, the improper integration fraction is reduced to a proper fraction by dividing the numerator polynomial by the denominator polynomial.