How do you calculate the derivative of #(cos(t^2)+t) dt# from #t=-5# to #t=sinx#?
i think you mean this
We can use the Leibnitz Rule for differentiating under the integral sign
which simplifies considerably here to
if that seems overwhelming, we can look at the Fundamental Theorem of Calculus, specifically
this can be extended using the chain rule to
that's all we did here