How about finding the Taylor series for sin(x^2) and then integrate that series "term by term".
That is essentially the same thing as "since you know f', you can find f'', f''', etc." and plug those into the formula for Taylor's series. Of course, you cannot know the value of f itself at whatever point you centering this oh. That will be the "+ C" when you do the itegration using Kiwi Dave's method.