Integration?

Question

Consider F(x)= inegral from x to 2 of 1/ (1 + t^4) dt
Find F'(x) and F'(2)

Answer 1

Use the Fundamental Theorem of Calculus
if F(x) = integral from a to x [f(t) dt] then F'(x) = f(x)

S f(t) dt from x to 2 can be rewritten as
-S f(t) dt from 2 to x

F(X) = -S 1/(1+t^4) from 2 to x
F'(X) by FTC = -1/(1+x^4)
F'(2) = -1/17

Answer 2

F'(x) = -1/(1+x^4)

F'(2) = -1/(1+2^4) = -1/17