Solve the integral equation $f(x) = x + \lambda \int_0^1 f(z)\,dz$ Find a closed-form solution for $f(x)$ in the following equation
$$
f(x) = x + \lambda \int_0^1 f(z)\,dz
$$
where $\lambda$ is a constant
I tried integrating both sides from $0$ to $1$ but wasn't exactly sure where to go from there
$$
\int_0^1 f(x) = \int_0^1 \left[x + \int_0^1 f(z)\,dz\right] dx
$$

$f(x)-x$ is equal to the constant $k=\lambda \int_0^1f(z) dz$ and the rest is obvious.
