A good explanation for this can be found here
To summarize : The number N in int(N) is often confused by the maximum size allowed for the column, as it does in the case of varchar(N).
But this is not the case with Integer data types- the number N in the parentheses is not the maximum size for the column, but simply a parameter to tell MySQL what width to display the column at when the table's data is being viewed via the MySQL console (when you're using the ZEROFILL attribute).
The number in brackets will tell MySQL how many zeros to pad incoming integers with. For example: If you're using ZEROFILL on a column that is set to INT(5) and the number 78 is inserted, MySQL will pad that value with zeros until the number satisfies the number in brackets. i.e. 78 will become 00078 and 127 will become 00127. To sum it up: The number in brackets is used for display purposes.
In a way, the number in brackets is kind of usless unless you're using the ZEROFILL attribute.
So the size for the int would remain same i.e., -2147483648 to 2147483648 for signed and 0 to 4294967295 for unsigned (~ 2.15 billions and 4.2 billions, which is one of the reasons why developers remain unaware of the story behind the Number N in parentheses, as it hardly affects the database unless it contains over 2 billions of rows), and in terms of bytes it would be 4 bytes.
For more information on Integer Types size/range, refer to MySQL Manual