What is $D_i F(x)$ for $x \in int(A)$?

Question

If $A=[a_1,b_1] \times ..... \times [a_n,b_n]$ and $f: A \to \Bbb R$ is continuous, define $F: A \to \Bbb R$ by

$F(x)=\int_{[a_1,x_1] \times ..... \times [a_n,x_n]} f$.

What is $D_i F(x)$ for $x \in int(A)$?

Now we know $D_i F(x)= \lim _{h_i \to 0}\frac {\int_{[a_1,x_1] \times ..\times [a_i,x_i+h_i]... \times [a_n,x_n]} f - \int_{[a_1,x_1] \times ..... \times [a_n,x_n]} f}{h_i}$. Now can I calculate the limit?