Infinity symbol in latex

The infinity symbol in LaTeX is simply written as

$ \infty$

How to write limit in latex

\operatorname*{lim}_{x\rightarrow \inf} f(x) = y

How to write integral from minus infinity to plus infinity in LaTeX

Lower and higher limits to integrals can be set as

$ \int^{+\infty}_{-\infty} x \, dx $