The area of the region bounded by the parabola \( y=x^{2}+1 \) and the straight line \( x+y=3 \)...

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The area of the region bounded by the parabola \( y=x^{2}+1 \) and the straight line \( x+y=3 \) is given by
(A) \( \frac{45}{7} \)
(B) \( \frac{25}{4} \)
(C) \( \frac{\pi}{18} \)
(D) \( \frac{9}{2} \)
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