The 3^rd derivative of a function $f\left(x\right)\text{ is zero},\forall x$, if  $f\left(0\right)=1,f^1\left(1\right)=2,f^{11}\left(1\right)=-1$, then $f\left(x\right)$ is 

$f^{111}\left(x\right)=0$

On integrating $f^{11}\left(x\right)=c,f^{11}\left(1\right)=c\Rightarrow c=-1$

$f^{11}\left(x\right)=-1,f^1\left(x\right)=-x+d$

$f^1\left(1\right)=-1+d=2,d=3$

$f^1\left(x\right)=3-x$

$\begin{array}{l}f\left(x\right)=\frac{-x^2}{2}+3x+e\\ \Rightarrow f\left(0\right)=1\Rightarrow e=1\end{array}$

$f\left(x\right)=\frac{-x^2}{2}+3x+1$