\[ \int_{5}^{14} f(x) d x-\int_{5}^{7} f(x) d x=\int_{a}^{b} f(x) d x \] where \( a=\square \) and \( b=\square \)

To solve the given expression   ∫₅¹⁴ f(x) dx - ∫₅⁷ f(x) dx = ∫ₐᵇ f(x) dx, we can use the property of definite integrals that states:   ∫ₐᵇ f(x) dx = ∫ₐᶜ f(x) dx + ∫꜀ᵇ f(x) dx  (for a ≤ c ≤ b). Here, if we let a = 5, c = 7, and b = 14, then   ∫₅¹⁴ f(x) dx = ∫₅⁷ f(x) dx + ∫₇¹⁴ f(x) dx. Subtracting ∫₅⁷ f(x) dx from both sides gives:   ∫₅¹⁴ f(x) dx - ∫₅⁷ f(x) dx = ∫₇¹⁴ f(x) dx. Thus, comparing with the original equation, the values are:   a = 7   b = 14.