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,