Actually, there exist infinitely many anti derivatives of each of these functions which
can be obtained by choosing C arbitrarily from the set of real numbers For this reason
C is customarily referred to as arbitrary constant In fact, C is the parameter by
varying which one gets different anti derivatives (or integrals) of the given function More generally, if there is a function F such that 
F ( ) =
( )
d
x
f
x
dx
, ∀ x ∈ I (interval),
then for any arbitrary real number C, (also called constant of integration)
[
F ( ) + C]
d
x
dx
 = f (x), x ∈ I
INTEGRALS         289
Thus,
{F + C, C ∈ R} denotes a family of anti derivatives of f