  Given a $d$-dimensional array $A$, an update operation adds a given constant
$C$ to each element within a continuous sub-array of $A$. A query operation
computes the sum of all the elements within a continuous sub-array of $A$. The
one-dimensional update and query handling problem has been studied intensively
and is usually solved using segment trees with lazy propagation technique. In
this paper, we present a new algorithm incorporating Binary Indexed Trees and
Inclusion-Exclusion Principle to accomplish the same task. We extend the
algorithm to update and query sub-matrices of matrices (two-dimensional array).
Finally, we propose a general form of the algorithm for $d$-dimensions which
achieves $\mathcal{O}(4^d*\log^{d}n)$ time complexity for both updates and
queries. This is an improvement over the previously known algorithms which
utilize hierarchical data structures like quadtrees and octrees and have a
worst-case time complexity of $\Omega(n^{d-1})$ per update/query.
