Question: Let \(A\) be the area of the region that lies under the curve \(y=-x^{2}+2 x\), above the \(x\) -axis and between the vertical lines \(x=0\) and \(x=1\)

1. Estimate the area \(A\) by taking the sample points to be the left endpoints and using four approximating rectangles of equal width.
2. Set up an expression for the area \(A\) as a limit of sums. Evaluate the expression.
3. Express the area \(A\) in terms of a definite integral. Evaluate the integral.
4. Is your estimate in part (a) an underestimate or an overestimate?

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