# Integrating Polynomials

Integration can be thought of as the opposite of differentiation, although the fundamental theorem of calculus isn’t quite this simple.

Differentiating a polynomial term, such as , requires first multiplying down by the power then reducing the power by one. If , . Integration is the reverse process. Given , one can find y by integrating, i.e, increasing the power by 1 then dividing by the new power: .

Given any y, we can write its integral as

This is an indefinite integral, definite integrals also have limits. Integrating a power of x requires adding one to the power then dividing by the new power, i.e.

Notice that we have added c on the end – this is known as the integration constant. The reason this is required whenever integration is performed is because integration is the reverse process of differentiation – whenever a constant is differentiated it disappears. This constant must be brought back in when the reverse process is performed. We call it c conventionally; it represents any constant value.

**Example** – Integrate .