If the symbol b in this example does not evaluate to a number, a warning message is generated and the integral is returned unevaluated:

This shows a correct use of NIntegrate:

In a multidimensional integral, the warning message will include a point on the boundary of the region of integration:

If a symbolic limit of integration is needed in a definition, you can use a pattern to prevent the rule from being applied until a numerical value is inserted for the limit:

Unset the rule for f: