Concept of Anti Derivatives or Integration
The inverse process of derivatives is called anti–derivatives or integration.
“A function $$f\left( {\text{x}} \right)$$being given and it is required to find a second function$$\phi \left( {\text{x}} \right)$$ whose derivative with respect to x is$$f\left( {\text{x}} \right)$$, that is,
\[\frac{{\text{d}}}{{{\text{dx}}}}\left[ {\phi \left( {\text{x}} \right)} \right] = f\left( {\text{x}} \right)\]
Thus if
\[\frac{{\text{d}}}{{{\text{dx}}}}\left[ {\phi \left( {\text{x}} \right)} \right] = f\left( {\text{x}} \right)\]
Then
\[\int {f\left( {\text{x}} \right){\text{dx}} = \phi \left( {\text{x}} \right) + {\text{c}}} \]
The function $$\phi \left( {\text{x}} \right) + {\text{c}}$$, then is called the antiderivate or indefinite integral of $$f\left( {\text{x}} \right)$$.
Symbol of Integration:
The function $$f\left( {\text{x}} \right)$$is called the integrand and the symbol $$\int {} $$is called the integral sign.
Thus, $$\int {f\left( {\text{x}} \right){\text{dx}}} $$means that $$f\left( {\text{x}} \right)$$is to be integrated with respect to (w.r.t) ‘x’ and is read as “Integral of $$f\left( {\text{x}} \right)$$”. Where dx indicates the variable with respect to which $$f\left( {\text{x}} \right)$$is to be integrated.
Note:

In $$\phi \left( {\text{x}} \right) + c$$, where ‘c’ is called the constant of integration.

$$\frac{{\text{d}}}{{{\text{dx}}}}$$ and $$\int \cdots {\text{ dx}}$$are inverse operations of each other.