To find the $\phi(x)$ for particular value of x. 
Let $\phi(x)$ be solution of   $$x=\int_{0}^{x}\exp(x-t)\phi(t)dt, \quad x\gt0.$$
  Then $\phi(1)$ is given by 
  
  
*
  
*-1
  
*0
  
*1
  
*2
  

Now I know how to verify whether a function is solution of integral equation or not but here  I guess $\phi(x)=x$ gives $\phi(1)=1$.
Am I right? Please help me to find the correct option

Use Laplace method and get $\dfrac{1}{s^2}=\dfrac{1}{s-1}{\cal L}(\phi)$. Then find $\phi$.
