Studying an interesting article of Daniel Lichtblau, I consider a variation of an example from it, calculating an improper integral

```
Integrate(RealAbs(Sin(x - y))^(-2/3), {x, 0, Pi}, {y, 0, Pi})
```

`-((12 Sqrt((Pi)) Gamma(-(1/3)) HypergeometricPFQ({1/6, 1/2, 2/3}, {7/6, 7/6}, 1))/ Gamma(1/6))`

This is not very useful analytic expression, so

```
N(%)
```

`16.7126`

Then I compare that result with the numeric one

```
NIntegrate(RealAbs(Sin(x - y))^(-2/3), {x, 0, Pi}, {y, 0, Pi},
Exclusions -> {y == x}, AccuracyGoal -> 3, PrecisionGoal -> 3)
```

`22.8915`

The latest result is produced without any warning. How to explain so big difference between the numbers? Could this difference be decreased? Which result is more reliable?