The book reads as follows:
"Let $a(x)$ and $b(x)$ be square integrable functions defined on [$a , b$]. First we note that it follows from the elementary inequality
$|ab| \le 1/2 (a^2 + b^2)$
that the function $|ab|$ is integrable."
Where does this function come from? How do I derive it? Does it have to do with the Schwarz Inequality? What does this equation imply about square integrable functions and absolutely integrable functions?