Consider $I = \int^{14}_{8} e^{-x^4} dx$. Match each riemann sum. $I = \int^{14}_{8} e^{-x^4} dx$
We have $L_{1000}, L_{10}, R_{1000}$.
We have $I= 0.335, 0.368, 0.367$.
Match each sum with each $I$ value.
I know that the graph is decreasing and approaches $0$ on the interval $[8,14]$, so $R_n \leq \text{ Actual Area I} \leq L_n$.
I know $R_{1000} = 0.335$, as it is the number most away from the actual area $I$. 
I think $L_{10} = 0.367$ and $L_{1000} = 0.368$ since $1000$ rectangles is much more accurate then $10$ rectangles, and thus it will be more larger then the actual area $I$.
Is this correct? It's the first time I'm doing these types of questions so I'm not $100%$ sure.
(not real approximations)

Since the function is decreasing.
$L_n \ge \int_a^b f(x) dx \ge R_n$
The right sum is less than the true value.
The left sum is greater than the true value.
As $n$ gets larger $L_n$ gets closer to the true value.
Your logic is good there.
Except then $L_{n}\ge L_{n+1}$
