A more generic version allows you to parameterize based on the bound:

    newtype BoundedInt b = BoundedInt Int

    class Bound b where
      boundRange :: t b -> (Int, Int)

    fromBounded :: BoundedInt b -> Int
    fromBounded (BoundedInt x) = x

    toBounded :: Bound b => Int -> BoundedInt b
    toBounded x =
      let result = BoundedInt x
	  (minb, maxb) = boundRange result
      in if minb <= result && result <= maxb
	 then result
	 else error $ "Out of range: " ++ show x

    instance Bound b => Num (BoundedInt b) where
      abs = toBounded . abs . fromBounded
      negate = toBounded . negate . fromBounded
      signum = toBounded . signum . fromBounded
      x + y = toBounded (fromBounded x + fromBounded y)
      x - y = toBounded (fromBounded x - fromBounded y)
      x * y = toBounded (fromBounded x * fromBounded y)
      fromInteger = toBounded . fromInteger

This assumes you want exceptions for overflow. Nowadays, you can put numbers in the type system, obviating the need for a "Bound" class, but I'm not familiar with it yet. The implementation above will also silently overflow given large enough bounds.