Cleaning Stains on Linoleum or Vinyl Floors?

I rent an apartment, and I recently put an offer in on a house, but I'd like to clean my apartment very well to cut down on the costs of moving out. In my bathroom I have vinyl or linoleum flooring, in the kitchen also. In the bathroom next to the tub my flooring is kind of stained. Water must have gotten to it even though I tried hard not to let water out of the tub. Its like a yellowish stain.

Is there something that may get this out? Or are they gonna have to redo the floors? The trim near those areas is kind of worn too. I am not sure how to tell if it is mold or if it's cleanable. If it is mold, can it be cleaned? I know it says somewhere just to use water to clean the floors, but that's what I've done the whole time I've been there and it doesn't work. Any suggestions are great, or if you have any additional questions for me I'd be happy to answer them for you. Thanks.