If the displacements are allowed to approach zero, then the number of terms in the sum increases...

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If the displacements are allowed to approach zero, then the number of terms in the sum increases without limit, but the sum approaches a definite value equal to the area under the curve in given figure.

What is the net work done by varying force \( F(x) \) from position \( x_{i} \) to \( x_{f} \) ?
(a) \( \int_{x_{f}}^{x_{i}} F(x) d x \)
(b) \( \int_{0}^{x_{f}} F(x) d x \)
(c) \( \int_{x_{i}}^{x_{f}} F(x) d x \)
(d) \( \int_{x_{i}}^{0} F(x) d x \)
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