I would like to know which numerical integral method to use to effectively calculate the definite integral of this trigonometric function from intervals a=$0$ to b=$10^{1000}$.
$$\int_a^b \sin\left(100\pi \sqrt{x^2 + 31364}\right) dx$$
Wolfram alpha calculates the integral from $a=0$ to $b = \infty$ to be: $$-0.4195181238484021201299757464$$
How did they arrive at this solution?
I've tried the Simpsons method between two consecutive root values so as to generalize the integral behavior across the function roots, but the function is not really periodic.