Cannot use `Integral` in Newton solver

I want to solve a nonlinear PDE where I impose, instead of a boundary condition, that the integral over the domain is zero. I don't know how to express this – the way I tried leads to an error (see below).

Things work if I impose that the solution is zero at a particular point (that's the second term u(0)). When I replace this by sum(Integral()*u), I receive an error about an unimplemented function.

julia> using ApproxFun

julia> newton(u -> [u(-1)-u(1), u(0), u''-1], Fun(x->1))
Fun(Chebyshev(), [0.25, 2.77556e-17, 0.25])

julia> newton(u -> [u(-1)-u(1), sum(Integral()*u), u''-1], Fun(x->1))
ERROR: MethodError: no method matching space(::ApproxFun.DualFun{Fun{Chebyshev{…}, Float64, Vector{…}}, ConstantOperator{Float64, Chebyshev{…}}})

Closest candidates are:
  space(::Fun)
   @ ApproxFunBase ~/.julia/packages/ApproxFunBase/1mBis/src/Fun.jl:339
  space(::ProductFun)
   @ ApproxFunBase ~/.julia/packages/ApproxFunBase/1mBis/src/Multivariate/ProductFun.jl:293
  space(::LowRankFun, ::Integer)
   @ ApproxFunBase ~/.julia/packages/ApproxFunBase/1mBis/src/Multivariate/LowRankFun.jl:348

I'd be happy to implement something, but as I'm new to the code I would need some pointers. For example, which function with what signature should be implemented?

Start by reproducing the issue with the shown newton calls, then trace the Integral() constraint and the failing space(::ApproxFun.DualFun...) dispatch. Check the newton, Integral, and space entry points; done means the integral-constrained example runs without the MethodError and preserves the existing point-constraint behavior.