​ definite integral help

Let's let the function be x^2 + 1

Using the left hand rule to calculate the area.......we will have 5 rectangles with the following heights    1, 5, 17, 37, 65  ...  and the width of each is 2

So......the total area = 2[1 + 5 + 17 + 37 + 65]  = 250 sq units

Using the right hand rule and applying the same procedure we have rectangles with the following heights 5, 17, 37, 65, 101  .... and the width of each is 2

So.....the total area = 2 [ 5 + 17 + 37 + 65 + 101] = 450 sq units

The actual area =   [10]^3/3 + 10  = 343+ 1/3 sq units

So

L₅ < actual  area < R₅