No, $P(X<1)$ is different from $P(|X|<1)$. After all $-2 < 1$ but $|-2|$ isn't!
To get $P(|X|<1)$ you need to find this area:
. . .
While $P(X<1)$ would be this area:
Credit: I used the shadenorm function here, which was written by Tony Cookson. It looks like there's a similar function shade.norm in package asbio