Evaluate the following integrals as a limit of sums:

Formula used:

where,

Here, a = 3 and b = 5

Therefore,

Let,

Here, f(x) = 2 – x and a = 3

Now, By putting x = 3 in f(x) we get,

f(3) = 2 – 3 = -1

Similarly, f(3 + h)

= 2 – (3 + h)

= 2 – 3 – h

= -1 – h

In this series, -1 is getting added n times

Now take -h common in remaining series

Put,

Since,