No, $P(X<1)$ is different from $P(|X|<1)$.


To get  $P(|X|<1)$ you need to find this area:

![required area][1]

. . . 

While $P(X<1)$ would be this area:

![wrong area][2]


Credit: I used the shadenorm function [here](https://gist.github.com/tony91782/950812), which was written by Tony Cookson.

  [1]: https://i.sstatic.net/SaV05.png
  [2]: https://i.sstatic.net/yZ3l2.png