Whenever I have to multiply integers, I think of this little math song to the tune of "Row Row Row Your Boat" that my teacher taught me in 7th grade.
Remember:
Multiply and divide
Then look at the signs
Different signs are negative
Same signs are just fine (positive)
For example: -5 x 5 = -25 -5 x -5 = 25
Different signs Same signs (positive & positive)
So in your specific case, the product of any integer and -1 depends. If the integer is positive, than the final product would be the integer in it's negative form. If the integer is negative, than the final product would be the integer in it's positive form.
I hope this makes sense to you!