How to Solve an Integration By Parts Problem?

[themadhatter1]

Homework Statement

Homework Equations

The Attempt at a Solution

I tried this problem and couldn't figure it out so I went and got the solution. However, I don't understand step 6 of the solution. I'm not sure how

$$(n-1)\int\sin^{n-2}x(1-\sin^2x)dx=(n-1)\int\sin^{n-2}dx-(n-1)\int\sin^nx dx$$

 

[themadhatter1]

Never mind, I've found my stupid mistake. Distributive Property!