\documentclass[]{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[upright]{fourier}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{amsmath,tkz-fct}
\usepackage[frenchb]{babel}
\definecolor{fondpaille}{cmyk}{0,0,0.1,0}
\tkzSetUpColors[background=fondpaille,text=Maroon]
\begin{document}
\begin{tikzpicture}[scale=2]
\tkzInit[xmin=0,xmax=4,ymin=-1,ymax=2]
\tkzAxeY[label=$f(x)$]
\tkzDefPoint(1,0){a}
\tkzFct[id=ln,domain=0.15:4,color=blue]{log(x)}
\tkzArea[top color=red!80,bottom color=gray!20,domain=1:2.718]
\tkzText[style={draw},color= blue](2,-0.8){$f(x)=\ln(x)$}
\tkzText[color= red](2.718,-0.2){$\text{e}$}
\tkzAxeX
\tkzDefPoint(2.718,1){b}
\tkzDrawPoints(a,b)
\tkzPointShowCoord(b)
\tkzText[draw](3.5,0.3){$\displaystyle
\mathcal{A}=\int_1^{\text{e}}\ln(x) dx$}
\tkzText(2,0.2){$\mathcal{A}$}
\end{tikzpicture}
\end{document}