The Dirichlet integral: $\displaystyle\int_0^\infty \frac{\sin x}{x}\,dx = \dfrac{\pi}{2}$. This classical result can be derived using the Laplace transform: $\int_0^\infty \frac{\sin x}{x}e^{-sx}\,dx = \arctan(1/s)$. Setting $s\to 0^+$ gives $\pi/2$.