The search for antiderivative of a given function on an interval, that is, the search for a function $F(x)$ for a given function $f(x)$ on an interval $I$ with the property that $F'(x)=f(x)$, is called finding the primitive or integrating. The following equality is valid for this primitive function $F$ and any $a$ and $x$ in $I$

$$F(x)=F(a)+ \int_a^x f(\xi)\,\dd \xi.$$ Every antiderivative (also called primitive) of $f(x)$ on $I$ can be written this way. One often denotes such a primitive function of $f(x)$ without lower and upper limits in the format $$\int f(x)\,\dd x$$ and then one callls it an indefinite integral. The indeterminacy lies in the fact that antiderivative of $f(x)$ is only uniquely determined up to a constant of integration. A simple example of an indefinite integral on $I=(-\infty,\infty)$ is $$\int (2x+3)\,\dd x = x^2+3x+c$$ where the constant of integration is denoted with the letter $c$. Many mathematical software programs such as the computer algebra systems Maple and Mathematica do not mention the constant of integration and provide only one primitive function.

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