Get the limit from

$\underset{x\to \mathrm{\infty}}{lim}(x{\int}_{\frac{\pi}{2}}^{\mathrm{arctan}\left(x\right)}\mathrm{sin}\left({t}^{2}\right)dt\phantom{\rule{mediummathspace}{0ex}})$

$\underset{x\to \mathrm{\infty}}{lim}(x{\int}_{\frac{\pi}{2}}^{\mathrm{arctan}\left(x\right)}\mathrm{sin}\left({t}^{2}\right)dt\phantom{\rule{mediummathspace}{0ex}})$