Compute the integral:

$$\underset{-\mathrm{\infty}}{\overset{\mathrm{\infty}}{\int}}{\displaystyle \frac{1}{{y}^{4}+1}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}y$$

$$\underset{-\mathrm{\infty}}{\overset{\mathrm{\infty}}{\int}}{\displaystyle \frac{1}{{y}^{4}+1}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}y$$