Issue with text and math expressions at the same time

Question

As some have guessed, there was indeed a \center before the title. As shown in the picture, I changed that to \begin{center} \end{center*} and the rest of the text is now aligned!

I tried to be more explicit regarding the first issue, as explained in the new picture.

Original Post:

My two problems are shown in the picture: I want the math expressions to appear in their "normal" size (i.e. not to fit into the line), but then when I have two expressions they don't get spaced as you can see. Another issue is that that piece of text that I marked with a * should be aligned to the left but instead appears in the center. Is there any way to resolve these issues?

In align* mode, there is no issue, since it would automatically add space between those two integrals, say. However, it is painful to write the text within \text{} and then to break the lines manually.

my TeXnic Center inputs:

\documentclass{article}
\usepackage[a4paper, margin=12mm]{geometry}
\usepackage[document]{ragged2e}
\usepackage{microtype}
\usepackage[fleqn]{mathtools}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{bigints}
\usepackage{physics}
\usepackage{wrapfig}
\usepackage{amsmath, graphics, setspace}
\usepackage{bm}
\usepackage{float}
\usepackage{hyperref}
\everymath{\displaystyle}
\setcounter{page}{1}
\setlength{\jot}{2mm}
\pagenumbering{arabic}
The community is here to help you with questions about TeX, LaTeX or related typesetting systems.  $\int_{-\infty}^\infty |P_\epsilon (t',\omega)|d\omega = |f(t')| \int_{-\infty}^\infty e^{-\omega^2 \epsilon^2} d\omega = |f(t')|\frac{\sqrt \pi}{\epsilon}$, The community is here to help you with questions about TeX.

And, $\int_{-\infty}^\infty |P_\epsilon (t',\omega)|dt' = e^{-\omega^2 \epsilon^2} \int_{-\infty}^\infty |f(t')| dt'$ The community is here to help you with questions about TeX, LaTeX or related typesetting systems.

Answer 1

I will interpret "I want the math expressions ... not to fit into the line" to mean that they should be typeset as displayed rather than as inline equations. If this interpretation is correct, you should replace the $...$ expressions with \[...\] expressions. \[ initiates an unnumbered displayed equation, and \] terminates it.

As some of the comments have already pointed out, the wisdom of the instruction \everymath{\displaystyle} is rather questionable. Speaking for myself, the only sensible justification for its use I can think of is in beamer documents. Even then, I'd think twice before I'd use it.

\documentclass{article}
\usepackage[a4paper, margin=12mm]{geometry} % <-- rather narrow margins
\usepackage[document]{ragged2e}
\usepackage{microtype}
\usepackage[fleqn]{mathtools}
\DeclarePairedDelimiter\abs\lvert\rvert % <-- new
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{bigints}
\usepackage{physics}
\usepackage{wrapfig}
\usepackage{%%amsmath, % 'mathtools' automatically loads 'amsmath'
   %%graphics, % don't load both graphicx and graphics
   setspace}
\usepackage{bm}
\usepackage{float} % are you sure you need this package?
\usepackage{xurl}  % for improved handling of URL strings
\usepackage{hyperref}
%%\everymath{\displaystyle} % highly questionable, except maybe in 'beamer' documents
%\setcounter{page}{1}       % that's the default
%\setlength{\jot}{2mm}
%\pagenumbering{arabic}     % that's the default
\begin{document}
The community is here to help you with questions about TeX, LaTeX 
or related typesetting systems.

[
\int_{-\infty}^\infty \abs{P_\epsilon (t',\omega)},d\omega 
  = \abs{f(t')} \int_{-\infty}^\infty e^{-\omega^2 \epsilon^2} d\omega 
  = |f(t')|\frac{\sqrt \pi}{\epsilon},. 
]

The community is here to help you with questions about TeX.
And, 
[
\int_{-\infty}^\infty \abs{P_\epsilon (t',\omega)},dt' 
= e^{-\omega^2 \epsilon^2} \int_{-\infty}^\infty \abs{f(t')},dt'.
] 
The community is here to help you with questions about TeX, LaTeX 
or related typesetting systems.
\end{document}