Let f(x)=x^2+x-2
Calculate R3 and L3 over [2,5].

What is R3 and L3?

Reading in context from your other post in the homework help forum, I think this means you're supposed to estimate the area under the curve by dividing it into three rectangles (essentially approximating the curve piecewise). The height of the rectangles is determined by the value of the function immediately to the left of the function for the "L" case, or the right of the function for the "R" case.

Since the interval is [2,5], you'd divide it into three even chunks: [2,3], [3,4], and [4,5]. The first thing to do is evaluate the function at each of the various x values:

f(2) = 4
f(3) = 10
f(4) = ?
f(5) = ?

For the "L" case, the first rectangle would have a height determined by the function value at its left edge (i.e. when x=2). So it would have a height of 4, the second rectangle would have a height of 10, etc. To find the area of each rectangle, you multiply its height by its width. The first rectangle, for example, has a height of 4 and a width of 1, so its area is 4. The second has an area of 10. Etc. If you add up the areas of all three rectangles, you'll have your "L3" approximation for the area under the curve.

For the "R3" case, you do the same thing, only the height of the rectangles is determined by the function value at the right side of the interval. So the first rectangle would have a height of 10 in this case.

The average of L3 and R3 will be a much better approximation of the area under the curve than either one by itself.