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**Ruun** In a definite integral (i.e., with limits for the variable(s) that you're integrating with respect of), there are no integration constants.

Example:

$\displaystyle \int_{-1}^{-3}5dx=\frac{5}{2}x^2$ and now you evaluate the function, in virtue of Barrow's Rule: $\displaystyle 5\left(\frac{-1^2}{2}-\frac{-3^2}{2}\right)$

In the other hand, if your integral is $\displaystyle \int 5dx=\frac{5}{2}x^2 + C_{0}$ where $\displaystyle C_{0}=f(t_{0})$ for some $\displaystyle t_0$ in the domain of the function.