Please explain result

[Arno K]

Found bounded-function in an xcas document:
For regular series expansion, order_size is a bounded function, but for non
regular series expansion, it might tend slowly to infinity, for example like a power of ln(x).
So its left over by the tried taylor expansion of sin(x) to get the integral done, then simply returned as the result, but the argument isn't explained.
Arno