If we have a function $g\colon \mathbb{N}^{k+1} \to \mathbb{N}$  which is primitive-recursive. How to show that the function $f\colon \mathbb{N}^{k+1} \to \mathbb{N}$ with$$f(x_1, \dots, x_k , x_{k+1})= \sum_{i=0}^{x_{k+1}}g(x_1,\dots, x_k,i)$$is also primitive recursive?
How to show that certain summations are primitive recursive?
computability;closure properties;recursion;primitive recursion