Evaluate the following integrals as a limit of sums:

Formula used:

where,

Here, a = 0 and b = 2

Therefore,

Let,

Here, f(x) = x² + 4 and a = 0

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

f(0) = 0² + 4 = 0 + 4 = 4

f(h)

= (h)² + 4

= h² + 4

Similarly, f(2h)

= (2h)² + 4

In this series, 4 is getting added n times

Now take h² common in remaining series

Put,

Since,