$\int_0^\infty\frac{\sin x}{x}\,dx=\frac\pi2$

Show that \(\int _ { 0 } ^ { \infty } { \frac { \sin { x } } { x } } d x = { \frac { \pi } { 2 } }\)

[For a Hint, see textbook by Stein and Shakarchi p64, #2]