Discussion
The area between \( y = x \) and \( y = x^{2} \) from \( x = 0 \) to \( x = 1 \) is
Answer: D
On this interval the line lies above the parabola, so integrate the difference:
\[ \int_{0}^{1}\left(x - x^{2}\right)dx \;=\; \left[\frac{x^{2}}{2} - \frac{x^{3}}{3}\right]_{0}^{1} \;=\; \frac{1}{2} - \frac{1}{3} \;=\; \frac{1}{6}. \]
The separate areas are \( 1/2 \) and \( 1/3 \), and taking either alone is the usual slip
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