How do I do a fast cumulative integration

Specific Domains Numerics
5

ApproxFun does this:

julia> f = Fun(x->exp(-x^2),0..5);

julia> g = 2/sqrt(π)*integrate(f); h = g - g(0);

julia> x = 0:0.5:5; [f.(x) h.(x)]
11×2 Matrix{Float64}:
 1.0         0.0
 0.778801    0.5205
 0.367879    0.842701
 0.105399    0.966105
 0.0183156   0.995322
 0.00193045  0.999593
 0.00012341  0.999978
 4.78512e-6  0.999999
 1.12535e-7  1.0
 1.60523e-9  1.0
 1.3888e-11  1.0

For a univariate function, I doubt you will be able to do much better.

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