Có bao nhiêu số thực $a$ thỏa mãn...

$\begin{aligned}
& \int\limits_{0}^{1}{\dfrac{x}{{{x}^{2}}+a}}\text{d}x=\dfrac{1}{2}\Leftrightarrow \dfrac{1}{2}\int\limits_{0}^{1}{\dfrac{2x}{{{x}^{2}}+a}}dx=\dfrac{1}{2}\Leftrightarrow \operatorname{l}\left. n\left| {{x}^{2}}+a \right| \right|_{0}^{1}=1\Leftrightarrow \ln \left| 1+a \right|-\ln \left| a \right|=1 \\
& \Leftrightarrow \ln \left| \dfrac{1+a}{a} \right|=1\left( a\ne 0 \right)\Leftrightarrow \left| \dfrac{1+a}{a} \right|=e\Leftrightarrow \left[ \begin{aligned}
& \dfrac{1+a}{a}=e \\
& \dfrac{1+a}{a}=-e \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& a\left( e-1 \right)=1 \\
& a\left( e+1 \right)=-1 \\
\end{aligned} \right.\Leftrightarrow \left[ \begin{aligned}
& a=\dfrac{1}{e-1} \\
& a=\dfrac{-1}{e+1} \\
\end{aligned} \right. \\
\end{aligned}$
Vậy có hai số thực a thỏa mãn.