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
$\displaystyle \int x^2 \, dx$
We can say that the anti-derivative of $\displaystyle x^2$ is $\displaystyle \frac{x^3}{3}$. However, another anti-derivative could be $\displaystyle \frac{x^3}{3} + 1$, or perhaps $\displaystyle \frac{x^3}{3} - \pi$. This is because the derivative of a constant is zero.
To remove all this ambiguity we say that $\displaystyle \int x^2 \, dx = \frac{x^3}{3} + C$, where C is an arbitrary constant.