## Differrentiating and Integrating Odd and Even Functions

The condition for functions to be odd or even are
$f(x)=-f(-x)$

$f(x)=f(-x)$

respectively.
When you differentiate these equations you get
$f'(x)=--f'(-x)=f'(-x)$
(1)
$f'(x)=-f'(-x)$
(2)
Differentiating an odd function gives an even function and vice versa. The same is not true when integrating in general, because of the role of the arbitrary constant .Integrating(1)and(2)gives
$f(x)=-f(-x)+c$

$f(x)=f(-x)+c$

so the odd and even conditions fail without the further condition that
$c=0$
.