There are three issues I can think he might be talking about:
1) if you get a solution, can you be sure that it's right? in this case, the neural network might spit out a wrong solution to the integral. However, this solution is easy to verify by just differentiating (which they do in the paper), so I don't think there's a problem here.
2) will the method always return a good answer? I don't think this is a requirement; Mathematica sometimes fails to integrate but people accept that.
3) Does the method work for larger, more interesting families of functions than the limited families tried in the paper? I think this is what Gibou is talking about, and seems like the strongest objection. This technique might just fail in some circumstances for reasons that are hard to anticipate.
no false positives (except for rare bugs); it will usually either return some partial solution (like a simplified version of the input), or else just keep running for a very long time until you give up.
1) if you get a solution, can you be sure that it's right? in this case, the neural network might spit out a wrong solution to the integral. However, this solution is easy to verify by just differentiating (which they do in the paper), so I don't think there's a problem here.
2) will the method always return a good answer? I don't think this is a requirement; Mathematica sometimes fails to integrate but people accept that.
3) Does the method work for larger, more interesting families of functions than the limited families tried in the paper? I think this is what Gibou is talking about, and seems like the strongest objection. This technique might just fail in some circumstances for reasons that are hard to anticipate.