\documentclass[a4paper, 12pt ]{article}  
\usepackage{tikz}  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{tikzpicture}
[line cap=round,line join=round,x=1cm,y=1cm,]
\draw[-latex,color=black] (-1,0) -- (5,0);
\draw[-latex,color=black] (0,-1) -- (0,3);
     \draw[  domain=0.5:4.5] plot(\x,{1/(\x)}) ;
     \draw[  domain=0.5:4.5] plot(\x,{(-1)/(\x)}) ;
    \draw[](1,-1.5)--(1,2);
    \draw[](4,-1)--(4,2);
   \node at (1,-0.3) [ ] {\small $1$};
         \node at (4,-0.3) [ ] {\small $4$};
           \fill[blue, opacity=0.7 ] plot[domain=1:4](\x,{(-1)/(\x)})--(4,0)--(1,0)--cycle;
            \fill[blue, opacity=0.7 ] plot[domain=1:4](\x,{1/(\x)})--(4,0)--(1,0)--cycle;
\end{tikzpicture}
\end{document}