I want to prove
$$\displaystyle\int_0^{\infty} \frac{\sin x}x \,\mathrm{d}x = \frac \pi 2$$
and
$$\displaystyle\int_0^{\infty} \frac{|\sin x|}x \,\mathrm{d}x \to \infty$$
And I found in wikipedia, but I don't know, can't understand. I didn't learn differential equations, Laplace transforms, and even inverse trigonometric functions.
So tell me easy, please.