What is the difference between Int and Integer?

"Integer" is an arbitrary precision type: it will hold any number no matter how big, up to the limit of your machine's memory…. This means you never have arithmetic overflows. On the other hand it also means your arithmetic is relatively slow. Lisp users may recognise the "bignum" type here.

"Int" is the more common 32 or 64 bit integer. Implementations vary, although it is guaranteed to be at least 30 bits.

Source: The Haskell Wikibook. Also, you may find the Numbers section of A Gentle Introduction to Haskell useful.

Int is Bounded, which means that you can use minBound and maxBound to find out the limits, which are implementation-dependent but guaranteed to hold at least [-2²⁹ .. 2²⁹-1].

For example:

Prelude> (minBound, maxBound) :: (Int, Int)
(-9223372036854775808,9223372036854775807)

However, Integer is arbitrary precision, and not Bounded.

Prelude> (minBound, maxBound) :: (Integer, Integer)

<interactive>:3:2:
    No instance for (Bounded Integer) arising from a use of `minBound'
    Possible fix: add an instance declaration for (Bounded Integer)
    In the expression: minBound
    In the expression: (minBound, maxBound) :: (Integer, Integer)
    In an equation for `it':
        it = (minBound, maxBound) :: (Integer, Integer)

Int is the type of machine integers, with guaranteed range at least -2²⁹ to 2²⁹ - 1, while Integer is arbitrary precision integers, with range as large as you have memory for.

https://mail.haskell.org/pipermail/haskell-cafe/2005-May/009906.html

Int is the C int, which means its values range from -2147483647 to 2147483647, while an Integer range from the whole Z set, that means, it can be arbitrarily large.

$ ghci
Prelude> (12345678901234567890 :: Integer, 12345678901234567890 :: Int)
(12345678901234567890,-350287150)

Notice the value of the Int literal.