% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage{tikz,xintexpr}

\begin{document}

\begin{tikzpicture}[line join=bevel,x=2cm,y=2cm]
	\draw[thin,lightgray,xstep=0.2,ystep=0.2] (-1.1,0) grid (1.2,1.5) ;
	\filldraw[fill=brown!70!black,fill opacity=0.85] (-1,0) -- plot[samples=500,domain=-1:1] (\x,{\xintfloateval{(1-(\x)^2)*exp(\x)}}) -- (1,0) -- cycle ;
	\draw[thick,->,>=latex] (-1.1,0)--(1.2,0) ;
	\draw[thick,->,>=latex] (0,-0.15)--(0,1.5) ;
	\draw (0,0) node[below left] {$O$} (-1,0) node[below] {$-1$} (1,0) node[below] {$1$} (0,1) node[left] {$1$} ;
	\draw (0.75,0.926) node[above right] {$\mathcal{C}_f$} ;
\end{tikzpicture}

\end{document}