Calculating Infinite Real Integrals Using Residues

Question

I want to calculate the following real integral using residues and I am unsure how to proceed.

$$\int_{-\infty}^{+\infty}\frac{1- x^2}{1+ x^4} dx$$

I know I must change this to a contour integral so what I was thinking was to take the contour as the full circle but I do not know how to find the singularities so therefore do not know what residues to compute.

I would appreciate guidance

Answer 1

$$\int_{0}^{1}\frac{1-x^2}{1+x^4}\,dx = \int_{1}^{+\infty}\frac{x^2-1}{x^4+1}\,dx $$ hence the value of the integral is just $\color{red}{0}$.