# Definition:Primitive (Calculus)/Indefinite Integral

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## Definition

Suppose that the real or complex function $F$ is a primitive of the function $f$.

From the Fundamental Theorem of Calculus, it is apparent that to find the value of a definite integral for a function between two points, one can find the value of the primitive of the function at those points and subtract one from the other.

Thus arises the notation:

- $\displaystyle \int f \left({x}\right) \ \mathrm d x = F \left({x}\right) + C$

where $C$ is the arbitrary constant.

In this context, the expression $\displaystyle \int f \left({x}\right) \ \mathrm d x$ is known as the **indefinite integral** of $f$.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*: $\S 14$