How to specify integration borders for Integro-Differential equation?

Hello, first-time user here.
I plan to solve the integro-differential equation:

$$\frac{d^2}{d\alpha^2} \phi(\alpha,\rho) - [\beta+f(\alpha,\rho)]\phi(\alpha,\rho) - f(\alpha,\rho) \int_{|\pi/3 - \alpha|}^{\pi/2 - |\pi/6-\alpha|} d\alpha' \phi(\alpha',\rho) = 0$$
My goal is to find the eigenvalue $\beta = \beta(\rho)$, and the eigenfunction $\phi(\alpha,\rho)$, where $\rho$ is an external parameter, and $\alpha \in [0,\pi/2]$
For now, let's forget about the function $f$, i.e. $f = 1$.

In the documentation (https://juliaapproximation.github.io/ApproxFun.jl/latest/usage/operators/#Algebraic-manipulation-of-operators), there is some information on how to deal with integrals, however the borders seem to be fixed at -1 and 1. Is there a way (and how) to provide the integration borders as in my case?

Any help is appreciated.

Start with the Algebraic manipulation of operators section in the ApproxFun.jl documentation, especially its treatment of integral operators on [-1, 1]. Determine how integration bounds are represented and whether the requested alpha-dependent bounds can be expressed there. Done means documenting or enabling a way to specify the stated bounds for alpha in [0, pi/2].