Evaluate the following integrals as a limit of sums:

We know,

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,