Practical guide and verification
Define the range precisely
Decide whether both endpoints are inclusive and whether duplicates are allowed. Those choices change the possible outcomes, especially when drawing several integers from a small range.
Uniform is not the same as unpredictable
A generator can distribute values uniformly without being suitable for passwords, keys, lotteries or other security-sensitive use. Cryptographic unpredictability is a separate requirement from statistical-looking output.
Common mistake
Do not repeatedly redraw until a preferred result appears and then describe the outcome as an unbiased random selection. The selection procedure needs to be fixed before the draw if fairness matters.