Pick a function $f(x)$ and either try to integrate its absolute value or try to integrate $\sqrt{f(x)}$ or $1/f(x)$.  This will require you to solve $f(x) = 0$.  And asking if there are any such solutions is undecidable for the class of functions you describe.


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**Edit** it's not clear for a few reasons why or if this would actually do the trick.