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The base of a solid is the region enclosed by the graphs of $y=x^{2}-5 x+7$ and $y=3$, between $x=1$ and $x=4$.$\newline$Cross sections of the solid perpendicular to the $x$-axis are rectangles whose height is $x$.$\newline$Which one of the definite integrals gives the volume of the solid?$\newline$Choose $1$ answer:$\newline$(A) $\int_{1}^{4}\left(x^{2}-5 x+4\right) \cdot x d x$$\newline$(B) $\int_{1}^{4}\left(-x^{2}+5 x-4\right) \cdot x d x$$\newline$(C) $\int_{1}^{4}\left(x^{2}-5 x+4\right)^{2} d x$$\newline$(D) $\pi \int_{1}^{4}\left(x^{2}-5 x+4\right)^{2} d x$