Evaluate the following integrals as a limit of sums:

Formula used:

where,

Here, a = 0 and b = 2

Therefore,

Let,

Here, f(x) = x² – x and a = 0

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

f(0) = 0² – 0 = 0 – 0 = 0

f(h)

= (h)² – (h)

= h² – h

Similarly, f(2h)

= (2h)² – (2h)

= (2h)² – 2h

Now take h² and -h common in remaining series

Put,

Since,