how do you calculate the instantaneous rate of change. is that the derivative.

Question

also:

if f is the antiderivate of
(x^2)/(1+x^5 such that f(1)=o then
f(4)=?

How would i find the integral of that? i don't even know what the first step is to get the answer. also, on this question, i can use the calculator but i don't what number i would need.

The answer choices are:
-0.012,0,.016,.376,0629. I'm thinking it's zero but i have no idea.

yes, instantaneous rate of change is the first derivative.
The second question can be integrated with the calculator here:

http://integrals.wolfram.com/index.jsp

Note the constant of integration does not appear, you have to solve for that with f(1)