Question

Does the value of a, when a does not equal b or a is greater than b, influence the result when using FTC 2?

Answer 1

the fundamental theorem of calculus, part 2 is derived using the assumption we are using the closed interval [a,b], so that a≤x≤b

However, see
http://tutorial.math.lamar.edu/Classes/CalcI/ProofIntProp.aspx#Extras_IntPf_Def1
the 3rd and 4th proofs show the effect of a>b or a=b
(i.e. in the first case we get the negative value of integrating in the "normal order" small to large, and in the second case a=b, we get 0 for the integral