Given that the describe doc string is `expect(...).to be_between`, it seems odd/wrong to use the negated form here.  Instead, you can do this:

``` ruby
it 'is exlcusive' do
  expect { expect(10).to be_between(1, 10) }.to fail
  expect { expect(1).to be_between(1, 10) }.to fail
end
```

(Again, showing both edges is important: otherwise, the implementation could actually be using `>=` for the low end, as there is no other spec enforcing the fact that it uses `>`).