My RPMs seem to go up to high before shifting into second gear as well as other gears why is this

So I just bought this Mitsubishi lancer 2002 its got 160k and starts fine shifts fine but I didn't realize until I give it a little extra gas that it revs really high before shifting into second and the Rpms reach between 4,000 and 5,000 also the check engine light is on, its actually a light that says service engine soon but there is no knocking noise or anything also it seems to be quite loud when I am giving it a little extra gas I'm not sure if its a bad loud I mean its like a race car loud and I looked at the exhaust Ans it looks like its stock. The people I bought it from said it needs a tune up so I was also wondering if maybe that would help with this problem or typically have absolutely nothing to do with it, hopefully you guys can help I really appreciate past questions you guys have answered and u guys really do your job well. Thanks in advance!