(Solution) - In Problems find the area of the region under the -(2025 Original AI-Free Solution)

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In Problems, find the area of the region under the curve y = f (x) over the interval [a, b]. To do this, divide the interval [a, b) into n equal subintervals, calculate the area of the corresponding circumscribed polygon, and then let n ??. (See the example for y = x2 in the text)
(a) y = x + 2; a = 0, b = 1
(b) y = ½ x2 + 1 ; a = 0, b = 1