A) 4/5
B) 5/4
C) 4/3
D) 3/4
E) 2/3
Correct Answer: C
Solution :
Let\[I=\int_{-1}^{1}{\frac{17{{x}^{5}}-{{x}^{4}}+28{{x}^{3}}-31x+1}{{{x}^{2}}+1}}dx\] \[I=\int_{-1}^{1}{\frac{17{{x}^{5}}+29{{x}^{3}}-31x}{{{x}^{2}}+1}}dx-\int_{-1}^{1}{\frac{{{x}^{4}}-1}{{{x}^{2}}+1}}dx\] \[=-2\int_{0}^{1}{\frac{({{x}^{2}}-1)({{x}^{2}}+1)}{({{x}^{2}}+1)}}dx\] \[=2\left[ \left( \frac{{{x}^{3}}}{3}-x \right) \right]_{0}^{1}=-2\left[ \frac{1}{3}-1 \right]\] \[=\frac{4}{3}\]
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