Based on the DescTools `AUC`

function. It can calculate the area under the
curve with a naive algorithm or a more elaborated spline approach. The curve
must be given by vectors of xy-coordinates. This function can handle unsorted
x values (by sorting x) and ties for the x values (by ignoring duplicates).

## Arguments

- x
Vector of x values.

- y
Vector of y values.

- method
Method to compute the Area Under the Curve (AUC). Can be

`"trapezoid"`

(default),`"step"`

or`"spline"`

. If "trapezoid", the curve is formed by connecting all points by a direct line (composite trapezoid rule). If "step" is chosen then a stepwise connection of two points is used. For calculating the area under a spline interpolation the splinefun function is used in combination with integrate.- ...
Arguments passed to or from other methods.

## Examples

```
library(bayestestR)
posterior <- distribution_normal(1000)
dens <- estimate_density(posterior)
dens <- dens[dens$x > 0, ]
x <- dens$x
y <- dens$y
area_under_curve(x, y, method = "trapezoid")
#> [1] 0.498307
area_under_curve(x, y, method = "step")
#> [1] 0.499534
area_under_curve(x, y, method = "spline")
#> [1] 0.498307
```