If the curve $f\left(x\right)=$$\int e^{x}dx$ passing through $\left(0, 1\right)$ then the ascending order of $f\left(0\right), f\left(1\right), f\left(-1\right), f\left(2\right)$ is 

$f\left(x\right)=$$\int e^{x}dx$

$=e^x+c$

$$\begin{gathered} pas\sin g through \left(0, 1\right) \\ \Rightarrow f\left(0\right)=e^0+C \\ \Rightarrow 1=1+c \\ \Rightarrow c=0 \\ \therefore f\left(x\right)=e^x \\ f\left(0\right)=e^0=1, f\left(1\right)=e, f\left(-1\right)=e^{-1}=\frac{1}{e}, \\ f\left(2\right)=e^2 \end{gathered}$$

$$\begin{gathered} Ascending order is \frac{1}{e}, 1, e, e^2 \\ \Rightarrow f\left(-1\right), f\left(0\right), f\left(1\right), f\left(2\right) \end{gathered}$$