Help with simple integral

[Ry122]

Could someone please explain to me why this is split into two separate terms?

http://img689.imageshack.us/img689/3092/unledwyx.png [Broken]

 

[Mark44]

Could someone please explain to me why this is split into two separate terms?

http://img689.imageshack.us/img689/3092/unledwyx.png [Broken]

Because it's quite a bit simpler to integrate t sin(at) than to integrate (6 - 3t)sin(at). In both cases you need to use integration by parts, but the simpler integrand makes the process easier.