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By definition definite integral is determined only up to integration constant. When integral depends on parameters constant of integration also depends on parameters. Some choices of integration constant may lead to undesirable results. For example:

integrate(x^n, x)

\label{eq1}{x \ {{e}^{n \ {\log \left({x}\right)}}}}\over{n + 1}(1)
Type: Union(Expression(Integer),...)
integrate(sinh(a*x), x)

\label{eq2}{\cosh \left({a \  x}\right)}\over a(2)
Type: Union(Expression(Integer),...)

In both cases integration constant have singularity, first for n = -1, second for a = 0, while there is choice of integration constant which avoids such singularity. Namely, in the first case (x^{n+1} - 1)/(n + 1) have removable singularity at n = -1, in the second case (\cosh(ax) - 1)/a have removable singularity at a = 0. However even with such choice of integration constant simply plugging in parameter to indefinite integral does not work, we get division by zero during evaluation (see Division by zero during evaluation).

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