I am currently practicing taking the derivatives of functions and I am familiar with the rules, but when it comes to integrals I am stuck.
For example:
$$g(x) = \int_{1}^{x^4} \sec{t} \, dt $$
In the book they say to use the chain rule, but what exactly are we applying the chain rule to? Are we applying the chain rule to $$\sec(t)$$ or are we applying it to the upper limit $$x^4 ?$$
I am just confused because the book substitutes the upper limit with the letter u which leads me to believe they are taking the chain rule of the upper limit, but why do that?