Question

Let $f$, be a continuous function in $[0,1]$, then $\lim _{n \rightarrow \infty} \sum_{j=0}^{n} \frac{1}{n} f\left(\frac{j}{n}\right)$ is
(A) $\frac{1}{2} \int_{0}^{\frac{1}{2}} f(x) d x$
(B) $\int_{\frac{1}{2}}^{1} f(x) d x$
(C) $\int_{0}^{1} f(x) d x$
(D) $\int_{0}^{\frac{1}{2}} f(x) d x$

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