Show that the limits $$\lim_{a \rightarrow +\infty} \int_0^a \sin(x^2) \mathrm{d}x \text{ and } \lim_{a \rightarrow +\infty} \int_0^a \cos(x^2) \mathrm{d}x$$ exist and are finite.
Show that the limits
$$\lim_{a \rightarrow +\infty} \int_0^a \sin(x^2) \mathrm{d}x \text{ and } \lim_{a \rightarrow +\infty} \int_0^a \cos(x^2) \mathrm{d}x$$
exist and are finite.