confusion about "find C such that the integral is convergent"

I have a question that tells me to find C such that the integral is convergent and I'm a bit confused on how it is convergent. If I'm asked to find the integral between 0 and infinity of f(x) - g(x), if the integral of f(x) within the range 0 to infinity is infinity, then even if the integral of g(x) is a constant, because f(x) is infinity, isn't the final answer still infinity? how can it be convergent?