Compute the spectrum for a operator 
Find the spectrum of the operator 
  $$
\begin{split}
A & \colon C[0,1] \rightarrow C[0,1] \\ 
  & f  \mapsto (Af)(x) := f(x) + \int_0^x f(t)dt 
\end{split}
$$

P.S.: I know the spectrum of $A_1\colon f  \mapsto \int_0^x f(t)dt$ 

The spectrum comes from analyzing $A-\lambda I$. Since $A = A_1+I$, you can see that $A-\lambda I = A_1-(\lambda-1)I$. It follows that $\sigma(A) = \sigma(A_1) +\{1\}$.
