I’ve heard that AP Chemistry does a terrible job of being the equivalent of a full year college level general chemistry class for those who intend to take chemistry further (not my opinion, just what people have told me).
So, does this apply to AP Calc AB covering the first semester of Calc (Calc I)? If I were to get a 4 or 5 on the AP Calc exam, should I be able to go to Calc II and be reasonably safe?
Most would be OK in terms of material covered, but you probably want to try the college’s old calculus 1 final exam to check your knowledge against the college’s expectations. (You can do this with chemistry as well if you intend to take more chemistry courses.)
Be aware that college math will cover material faster than high school calculus AB.
And AP chemistry only covers one semester of college chemistry.
AP Chem is pretty comparable to Honors Inorganic Chem at my school (prelims/finals were basically AP questions.
For a CS major, you’ll probably have to take classes like Calc II, Calc III (maybe Calc I although I think colleges mainly start off with II), Linear Algebra, Diff EQ etc. Calc II is essentially AP Calc BC. If you only have AB credit, you’d probably be better starting off with Calc II and working from there.
In any respect, no AP covers a full year of material.
Calculus BC approximates a year’s worth of single variable calculus material (calculus 1 and calculus 2) as commonly taught in college. A few colleges may cover more material in their calculus courses than is typical.
Don’t listen to some of these people. The answer is it honestly depends. I learned WAY more in AP Chemistry than I did the first semester of college chem, and I go to a good school. My high school just did a good job teaching it I guess. As for calc, I had A’s all throughout AP Calculus, and I found that it basically was the same level of difficulty as all my other Calc courses (multivariable included). If you liked AP Calc AB, odds are you ae going to be extremely successful in all the calculus courses and probably beyond! So don’t sweat it! I was in the same boat last year and trust me, it’s nothing to worry about 
Different schools cover different amount in their AP curriculum, and different universities cover different things in their intro chem (calc is a bit more consistent). Your best bet is to compare your high school’s and college’s syllabi and use your own judgement as to how well you know the material that the intro classes cover. Even if two people took the same AP course, their comfort with the material and preparedness for the next level can vary. I ended up deciding to use all my AP credit (including a full year of chem credit) and had no problem, but I know others who regretted making that choice.