\begin{align*} 
E(\widehat{f}_{h}(x)) &=\int_{-\infty}^{\infty}K(z)f(x)dz - \int_{-\infty}^{\infty}K(z)h z f^{'}(x)dz \nonumber \\
&+\int_{-\infty}^{\infty}K(z)\dfrac{(hz)^{2}}{2}f^{''}(z)dz+o(h^{2})\\
&=f(x)\int_{-\infty}^{\infty}K(z)dz-hf^{'}(x)\int_{-\infty}^{\infty}zK(z)dz\\
&+\dfrac{h^{2}}{2}f^{''}(x)\int_{-\infty}^{\infty}z^{2}K(z)dz+o(h^{2})\nonumber \\
&=f(x)+\dfrac{h^{2}}{2}k_{2}f^{''}(x)+o(h^{2}).
\end{align*}