Evaluate the following integrals as a limit of sums:


Formula used:



where,



Here, a = -1 and b = 1


Therefore,





Let,



Here, f(x) = x + 3 and a = -1



Now, By putting x = -1 in f(x) we get,


f(-1) = -1 + 3 = 2


Similarly, f(-1 + h)


= -1 + h + 3


= h + 2



In this series, 2 is getting added n times



Now take h common in remaining series





Put,



Since,












4