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State the definite integral represented by the following limit:

$$\lim_{n\rightarrow \infty }\sum_{i=1}^{n}\left ( 3+\frac{2i}{n} \right )^{3}\left ( \frac{2}{n} \right )$$

$\int_{3}^{5}x^{3}dx$

$\int_{2}^{5}x^{3}dx$

$\int_{3}^{5}\left ( 1+x \right )^{3}dx$

$\int_{2}^{5}\left ( 1+x \right )^{3}dx$