Hi

I'm learning functional analysis (operator theory) and I found the following question and I have no idea what to do ( I figured it has something to do with adjoint operators)

Is there a continuous function $\displaystyle $f: [0,1] \rightarrow \mathbb{R}$ which solves the following equation and if yes is $\displaystyle $f$$ unique:

$\displaystyle f(x)+\int_0^x e^{x cos(t)}f(t)\ dt=x^2+1 \ x \in [0,1]$

Can you help me? Thank you very much !