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Considering the below equality (or equivalency), could someone please explain how the bounds and indices are shifted?

$$\sum_{i=2}^{k}(h_i/f_{i-1})=\int_{1}^{k}(h(i)/f(i))di$$

$$\sum_{i=2}^{k}(h_i/f_{i-1})=\int_{1}^{k}(h(i)/f(i))di$$

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