Recently, I have looked into nonelementary integrals and I have a question.(adsbygoogle = window.adsbygoogle || []).push({});

When looking at ∫sin(sinx)dx, which I know cannot be represented as an elementary function, I wondered what the function would look like. Using mathematica, I was able to get a graph of f(x)=∫_{0}^{x}sin(sinx)dx. Does the represent the same function as ∫sin(sinx)dx? And more importantly, why? (Sorry about the bad formating for limits of integration)

Edit: From what I've seen, it is if and only if the function g(x)=∫sin(sinx)dx is 0 at x=0. If this was true, then how would one go about proving if g(0)=0 or not?

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