Doesn't matter what the lower bound is as long as the antiderivative (F) is defined at that point. Because the lower point is fixed it yields a constant to the antiderivative and thus after differentiation it's gone. Example: $\frac{ d }{ dx }\int\limits_{1}^{x}\frac{ 1 }{ t } dt = \frac{ d }{ dx } (\ln \left| x \right| - \ln \left( 1 \right)) = \frac{ 1 }{ x }$ You could substitute any positive constant value in place of 1 and the result would have been just the same.