>The total emission intensity should be calculated like the photo(Integral Emissmition intensity(E) dE), right?

Yes, sure. Besides, the integral for the chart Intensity vs wavelength will give the same result (see that numbers are different for intensity vs quant energy and vs wavelength).

>Summation for discrete domain E or Integral for continuous domain E.

Numerical simulation often deals with discrete representation of continuous values. I mean integration, which means summation of products of i-th value and i-th mesh step. The mesh step is uniform for energy representation of spectrum, and non-uniform for the wavelength representation.

>Do you mean that the integrated emiision spectrum is proportional to J*IQE ?

Sure. That is why this function is not done. Besides, the result of integration is proportional to the current converted into the light, jrad (see Results table). Please find exact equations below

jrad = j * IQE = e * \int_0^\infty I(E) dE = e * \int_0^\infty I(\lambda) d\lambda

Here, I (E) and I(\lambda) are emission spectrum in energy and wavelength representation, and TEX notation is used (\int_0^\infty means integration from 0 to infinity).