calculus - How to prove that $int_{-infty}^{infty} frac{1-cos x}{x^2} dx$ equal to $pi$?

How to prove that $\int_{-\infty}^{\infty} \frac{1-\cos x}{x^2} dx$ equal to $\pi$?

Is there any simple approach that does not require knowledge in Fourier Analysis or Complex analysis?