Question

d/dx

Answer 1

Use the fundamental theorem of calculus for this, that tells you that:

Let \(H(x)\) and \(F(x)\) be anti-derivatives of \(g(t)\).\[H(x) = \int\limits_{x}^{5}g(t)dt = F(5) - F(x)\]

Then \[H'(x) = \frac{d}{dx}~\int\limits_{x}^{5}g(t)dt = F'(5) - F'(x) = g(5)-g(x)\]