Existence, Uniqueness & Bifurcations · Easy problem

Apply Picard iteration to $y' = y$, $y(0) = 1$, starting from $\varphi_0(t) = 1$ and using $\varphi_{n+1}(t) = 1 + \displaystyle\int_0^t \varphi_n(s)\,ds$. Evaluate $\varphi_2(2)$.