\int_0^{+\infty}\Big(\frac{1/2}{1+x}+\frac{-\frac{1}{2}x+\frac{1}{2}}{1+x^2}\Big)dx=\int_0^{+\infty}\frac{1/2}{1+x}dx+\int_0^{+\infty}\frac{-\frac{1}{2}x+\frac{1}{2}}{1+x^2}dx