= Solution
Assume the <spline knot sequence> is ordered and its relevant support spans satisfy $t_{i+k}>t_i$. For distinct knots, the <divided difference> is a finite linear combination of evaluations, so it commutes with integration. With $u\in[a,b]$,
$$
\int_a^b(u-t)_+^{k-1}\,dt=\int_a^u(u-t)^{k-1}\,dt=\frac{(u-a)^k}{k}.
$$
Taking the order-$k$ <divided difference> in $u$ gives
$$
\boxed{\int_a^bM_i(t)\,dt=k[t_i,\ldots,t_{i+k}]\frac{(u-a)^k}{k}=1}.
$$
Indeed, the order-$k$ <divided difference> of a degree-$k$ <polynomial> is its <leading coefficient>, here $1/k$. This proves the <unit-integral normalization of a B-spline>. Admissible repeated knots follow by coalescing knots, with the usual one-sided endpoint conventions.
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