Why is this answer wrong and how do you do it?

F'(x) = 2x eˣ¹⁴ − eˣ⁷

Step-by-step explanation:

You're close.  According to second fundamental theorem of calculus:

If F(x) = ∫ₐᵇ f(t) dt, then F'(x) = b' f(b) − a' f(a).

F(x) = ∫ₓˣ² eᵗ⁷ dt

F'(x) = (2x) e⁽ˣ²⁾⁷ − (1) e⁽ˣ⁾⁷

F'(x) = 2x eˣ¹⁴ − eˣ⁷

df =

both have same length