A) \[1+{{x}^{2}}\]
B) \[\frac{1-{{x}^{2}}}{2}\]
C) \[1-{{x}^{2}}\]
D) \[\frac{1+{{x}^{2}}}{2}\]
Correct Answer: D
Solution :
\[f(x)=\int\limits_{-1}^{0}{-t\,dt\,+\int\limits_{0}^{x}{t\,dt\,=\frac{{{x}^{2}}+1}{2}}}\]
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