{NotebookFileName[],DateString[]}

style[
t_
]:=
Style[t,Bold,FontFamily->"Arial",FontSize->14]

$Assumptions={{x,y}∈Reals}

Chain rule exercise

D[(∫_a^x)f[t]\[DifferentialD]t,x]

D[(∫_a^(u[x]))f[t]\[DifferentialD]t,x]

D[(((x-1)(x+1))/2),x]//Simplify

A couple examples

(∫_1^2)x\[DifferentialD]x

(∫_(-1)^1)(a (x^2)+b x+c)\[DifferentialD]x

a1[
t_
]:=
100 (2^(-t/1000))

∫a1[t]\[DifferentialD]t

∫a (2^(-t/th))\[DifferentialD]t

32*3125