antiderivative

The indefinite integral of a function \( f(x) \) is defined as the set of all its primitives, expressed as \( F(x) + c \), where \( c \) is an arbitrary real number. It is denoted as:

\[\int f(x) dx = F(x) + c \quad c \in \mathbb{R}\]

The definite integral of \( f(x) \) from \( a \) to \( b \) represents the signed area between the graph of \( f(x) \), the x-axis, and the lines \( x = a \) and \( x = b \) and is given by:

\[
\int_{a}^{b} f(x) \, dx
\]

The Fundamental Theorem of Calculus, establishing the precise link between differentiation and definite integration.

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