how to calculate Riemann Sums in R?

Question

Can any one help how to find approximate area under the curve using Riemann Sums in R?

It seems we do not have any package in R which could help.

Sample data:

MNo1    X1  Y1    MNo2  X2  Y2
1   2981    -66287  1   595 -47797
1   2981    -66287  1   595 -47797
2   2973    -66087  2   541 -47597
2   2973    -66087  2   541 -47597
3   2963    -65887  3   485 -47397
3   2963    -65887  3   485 -47397
4   2952    -65687  4   430 -47197
4   2952    -65687  4   430 -47197
5   2942    -65486  5   375 -46998
5   2942    -65486  5   375 -46998
6   2935    -65286  6   322 -46798
6   2935    -65286  6   322 -46798
7   2932    -65086  7   270 -46598
7   2932    -65086  7   270 -46598
8   2936    -64886  8   222 -46398
8   2936    -64886  8   222 -46398
9   2948    -64685  9   176 -46198
9   2948    -64685  9   176 -46198
10  2968    -64485  10  135 -45999
10  2968    -64485  10  135 -45999
11  2998    -64284  11  97  -45799
11  2998    -64284  11  97  -45799
12  3035    -64084  12  65  -45599
12  3035    -64084  12  65  -45599
13  3077    -63883  13  37  -45399
13  3077    -63883  13  37  -45399
14  3122    -63683  14  14  -45199
14  3122    -63683  14  14  -45199
15  3168    -63482  15  -5  -44999
15  3168    -63482  15  -5  -44999
16  3212    -63282  16  -20 -44799
16  3212    -63282  16  -20 -44799
17  3250    -63081  17  -31 -44599
17  3250    -63081  17  -31 -44599
18  3280    -62881  18  -38 -44399
18  3280    -62881  18  -38 -44399
19  3301    -62680  19  -43 -44199
19  3301    -62680  19  -43 -44199
20  3313    -62480  20  -45 -43999

Answer 1

Check this demo :

> library(zoo)
> x <- 1:10
> y <- -x^2
> Result <- sum(diff(x[x]) * rollmean(y[x], 2))

> Result
[1] -334.5

After check this question, I found function trapz() from package pracma be more efficient:

> library(pracma)
> Result.2 <- trapz(x, y)
> Result.2
[1] -334.5