Correct Answer: Option A

Explanation

Area bounded by
y = x² - x + 3 and y = 3
x² - x + 3 = 3
x² - x = 0
x(x -1) = 0
x= 0 and x = 1
\(\int^{1}_{0}\)(x² - x + 3)dx = [¹/₃x³ - ¹/₂x² + 3x]\(^1 _0\)
(¹/₃(1)³ - ¹/₂(1)² + 3(1) - (¹/₃(0)³ - ¹/₂(0)² + 3(0))
= (¹/₃ - ¹/₂ + 3)- 0
= \(\frac{2-3+18}{6}\)
= ¹⁷/₆

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