Indefinite Integrals

Indefinite Integrals

If F(x) is a function whose derivative F'(x) = f(x) on certain interval of the x-axis, then F(x) is called the anti-derivative of indefinite integral f(x). When we integrate the differential of a function we get that function plus an arbitrary constant. In symbols we write 

$\displaystyle \int f (x)\,dx = F(x) + C$

 
where the symbol $\displaystyle \int$, called the integral sign, specifies the operation of integration upon f(x) dx; that is, we are to find a function whose derivative is f(x) or whose differential is f(x) dx. The dx tells us that the variable of integration is x.