Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 0 and b = 2


Therefore,




Let,



Here, f(x) = x2 + 1 and a = 0




Now, By putting x = 0 in f(x) we get,


f(0) = 02 + 1 = 0 + 1 = 1


Similarly, f(h) = h2 + 1




In this series, 1 is getting added n times



Now take h2 common in remaining series





Put,



Since,
















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