How to find an antiderivative of f double prime x?

Question

For this question, wouldn't the answer just be $f'(4)-f'(1)$? I'm not exactly sure if I'm right or how to further solve this question. Can someone please help me out?

Suppose that $f(1)=2 ,f'(1) =5, f'(4) = 3$ and f'' is continuous. Find the value of $$\int_{1}^{4}f''(x)dx$$

Answer 1

For the Fundamental theorem of calculus

$$\int_{1}^{4}f''(x)dx=f'(4)-f'(1)=3-5=-2$$

Answer 2

The definite integral is $f'(4)-f'(1)$. As $f'(4)$ is unknown and unconstrained, the integral can be anything.