Fill integral exponent function

Question

I want to fill integral limits by exponent function y=e^{x-1}; y=2-x, and Ox. Please everybody help]1

Answer 1

First, you should post what you tried, and then, you post your question.

\documentclass[a4paper, 12pt]{standalone}
\usepackage{fouriernc}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns}
\pgfplotsset{compat=1.15}
\begin{document}
\begin{tikzpicture}
\begin{axis}
    [
    axis lines = center,
    axis line style = very thick,
    xlabel=$x$, ylabel=$y$,
    domain=-1:3,
    ymin=-0.5,
    ymax=2.5,
    xmin=-1,
    xmax=3,
    xticklabels={},yticklabels={},
    unit vector ratio*=1 1 1,
    width=7cm,
    grid=major,
    grid style={gray!30}
    ]
\addplot [name path=A,blue, very thick,samples=100] {exp(x-1)};
\addplot [name path=B,thick] {2-x};
\addplot [name path=C] {0};
\node at (axis cs:-0.25, -0.25) {$O$} ;
\addplot [black, mark = *] coordinates {(1, 1)} ;
\addplot[pattern=north east lines] fill between[of=A and C,soft clip={domain=0:1}];
\addplot[pattern=north east lines] fill between[of=B and C,soft clip={domain=1:2}];
\addplot[color=blue,dashed] coordinates {
            (0, 1)
            (1, 1)
            (1,0 )
               };
\node at (axis cs:-0.2, 1) {$1$} ;
\node at (axis cs:1, -0.25) {$1$} ;
       \end{axis}
\end{tikzpicture}
\end{document}