When I ask Wolfram Alpha to compute the integral of $\sin^2{x}$ with respect to $x$, one of the results it gives me is a Taylor series, but it includes a $O(x^8)$ term. What does it mean?
Taylor Series about $x=0$:
$$\frac{x^3}{3} - \frac{x^5}{15} + \frac{2x^7}{315} + O(x^8)$$