Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = 0 and b = 5


Therefore,




Let,



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




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


f(0) = 0 + 1 = 1


Similarly, f(h) = h + 1



In this series, 1 is getting added n times



Now take h common in remaining series





Put,



Since,













5