Use array_append function to append an element at the end of an array:
UPDATE table1
SET integer_array = array_append(integer_array, 5);
5 is a value of choice, it’s of an integer datatype in your case. You probably need some WHERE clause as well not to update the entire table.
Try below to see how it works:
SELECT ARRAY[1,2], array_append(ARRAY[1,2],3);
Result:
array | array_append
-------+--------------
{1,2} | {1,2,3}