anyway let me ask something more basic...why do we have a integrational constant in calculus? if we sum ( in summation) up the thing do we need any constant like this??
Consider the indefinite integral
We can say that the anti-derivative of is . However, another anti-derivative could be , or perhaps . This is because the derivative of a constant is zero.
To remove all this ambiguity we say that , where C is an arbitrary constant.