Riemann Sum Approximation (confused...)

Question

I'm having trouble determining when a left-hand approximation is an over/under estimate for a given function.

For example, for the graph above $f(x)$=$ln(x)$ and the function is increasing for all $x$ > 0.Since the function continues to increase, doe that mean the left-hand approximation would be an underestimate? $$\\$$ Update:

Answer 1

When the function is always increasing, that means the left-hand sum will be an underestimate and the right-hand sum will be an overestimate.

When the function is always decreasing, that means the right-hand sum will be an underestimate and the left-hand sum will be an overestimate. $$\\$$

For the function $f$($x$)=$ln$($x$), it is always increasing.

This site may help you understand better: http://www.shmoop.com/definite-integrals/compare-left-right-sum.html