Hello I tried but stuck in this question. I think an integrable function might be not continious.
Let $R = [a_1,b_1]\times...\times[a_n,b_n]$ be an $n$-dimensional rectangular region and $f: R \to \mathbb{R}$ be integrable. For each $x = (x_1,...,x_n)\in R$, define $R_x$ to be $[a_1,x_1]\times ... \times [a_n,x_n]$. Suppose $$F(x) = \int_{R_x}fdV$$ Show that the function $F: R \to\mathbb R$ is continious.
Any help is welcome.