PIDE over space with variable as **lower** limit of interval?

[fabern]

With MethodOfLines.jl I would like to solve a partial integro-differential equations (PIDE) of the following form:

$$ \frac{\partial}{\partial t}u(t,x) = -\frac{ \partial}{\partial x}\left[u(t,x) \int_x^{150}u(t, y)dy\right] - m(t,x)u(t,x), $$

where x is the independent/space variable and 150 some constant (xupper).
(I can still simplify this with the product rule, but the relevant part here are the limits of the integral.)
Note, that the integral limits are going from x to a constant xupper.

The documentation of MethodOfLines discusses a PIDE with limits, that are going from 0 to x:

$$ \frac{\partial}{\partial t}u(t, x)+2u(t, x)+5\frac{\partial}{\partial x}[\int_0^xu(t, x)dx]=1, $$

From a previous GitHub issue it appears different integration limits need to be handled manually.
Is this still the case?
Where/How would I need to add the integration with x as lower limit up to a constant xupper?

PS: I really enjoy discovering this package.

[fabern]

Just realizing that a test case had already been considered:

MethodOfLines.jl/test/pde_systems/MOL_1D_Integration.jl

Line 123 in f9da592

@testset "Test 02: Test integration with arbitrary limits, (a .. b)" begin

So, I might have a look at this PR 216 to see where it would need to be added. EDIT: I tried to understand the code from that previous PR, but I need to have some help for the extension.