How to find the area using Riemann's sum of sin(x^2) dx [0,1] where n=5

as in 5 boxes, with right end points.

I was looking through my notes and I must have copied down my formulas wrong because NOTHING is working for me. Please help!

Definite Integrals suck. I like the Indefinite Integral with Anti-derivatives much better.

First let us find delta(x)

(b - a)/n
(1 - 0)/5
delta(x) = 1/5

Since we are using right endpoints, we don't start with 0 as that would be starting with left endpoints. With right endpoints, we will start with delta(x).

So your points will be:

f(1/5), f(2/5), f(3/5), f(4/5), f(5/5)

Keep in mind that all you are doing at this point is just finding the length from the x axis to the curve; In other words you are finding y.
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In a Riemann Sum, you just multiply delta x by all of those answers like this:

delta(x) * [f(1/5) + f(2/5) + f(3/5) + f(4/5) + f(5/5)]

Since we know delta(x), we can go ahead and plug that in:

1/5 * [f(1/5) + f(2/5) + f(3/5) + f(4/5) + f(5/5)]

Now we just evaluate each of those f(x) values using sin(x^2)

sin((1/5)^2) + sin((2/5)^2) + sin((3/5)^2) + sin((4/5)^2) + sin(1)

Doing that I get:
(0.039989 + 0.159318 + .352274 + 0.597195 + .841471)
Summing all of that I get:
1.99025


So now we do:
1/5 [ 1.99025]

And the answer is:
.398049

you will not find the ' area ' , just an approximation to it

partition points are [ 0,0.2 , 0.4 , 0.6 , 0.8 , 1 ] and right endpoints means compute

[0.2] { sin (0.2)² + sin (0.4)² + sin (0.6)² + sin (0.8)² + sin 1 }