Feature request: add support for integrals

[sdwfrost]

I'd like to be able to define a variable as an integral of another variable over a dimension, something along the lines of:

@parameters t x
@variables y(t,x)
@derivatives Dt'~t
@derivatives Dx'~x
# define new variable which is the integral of y over x
Y(t) = sum(y[t,])

I'm not really fussy about the syntax for this however.

[ChrisRackauckas]

I think we want to make it match Symbolics.integral as a standard form for symbolic integrals, and have that do expand_integrals or something to actually integrate. Then we can use the un-expanded integrals as the form here.

JuliaSymbolics/Symbolics.jl#58

[lstagner]

I'm looking into solving the Grad-Shafranov Equation and this functionality is would be helpful as the BC's are given by an double integral.