Write a program to sort an array of integers.
Implement sort_integers(nums) to return the values in ascending order without relying on Python's built-in sorting function. The function receives a list of integers and returns a new sorted list, for example [3, 1, 2] becomes [1, 2, 3] and [4, -1, 4] becomes [-1, 4, 4]. Constraints: 0 <= len(nums) <= 1,000, and values range from -10^9 to 10^9.
def sort_integers(nums):