Why is the integral of 1/x^2 between the limits 1 and -1 equal to -2, despite the graph of y=1/x^2 being strictly positive? - Quora
![complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange](https://i.stack.imgur.com/3McmR.jpg)
complex analysis - Calculation of the $\int_{-\infty}^{\infty} \frac{dx}{1+x^2}$ using contour integration - Mathematics Stack Exchange
![complex analysis - Integrating $\int_0^\infty \frac{1-\cos x }{x^2}dx$ via contour integral. - Mathematics Stack Exchange complex analysis - Integrating $\int_0^\infty \frac{1-\cos x }{x^2}dx$ via contour integral. - Mathematics Stack Exchange](https://i.stack.imgur.com/XEqw9.png)