The derivative of an integral of a function is the function itself, so the integral is an anti-derivative. This can all be found on Google.
Taking chem w/o calc will not lead to knowledge and understanding of the physics involved and allow one to work with it on an intimate level. It is just memorization with no depth to the understanding. For instance, why the sky is blue. There's the simple explaination and there's the detailed one which allows one to answer many more seemingly unrelated questions.
Evolution isn't stressed much, but advancing though bio, biochem and med lit leads one to learn it w/o even being aware it is part of it.
" traits that were 'adaptations' to given environmental factors."
Traits just happen. If they work, they work. If not, they don't. Environment only effects the work, or don't work part. It does not cause, or drive traits to change, or appear. Changes in the regular sequence and/or components involved in the reactions effect traits. Only if the environment has certain chemicals that react, or effect the sequence copying does it have an effect.
There is no design involved. If it works, it does and otherwise not. Darwin is an old taxt that I never read and all I can say is that I think he suspected, or believed what I just wrote.
Once design enters the possibilities considered. One ends up with who designed it. God, who knew you before the world existed, does not and did not tinker with stuff to get you here. It all came about as a breath of creation into time. Once in time, the world became as it appears now as it appears to have by scientific study. Design takes away from that and leads to falsehoods, because the design was accomplished before the world was.