How to specify integration borders for Integro-Differential equation?

[lhapp27]

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.

[jishnub]

You need to set the domain to one that you want to integrate over. By default, the documentation mentions -1 to 1 because this is the domain for the canonical Chebyshev polynomials.