Plot the area under the curve (integral) of a set of x and y values in R

Question

I have a set of data points that I would like to plot the "integral" for.

For example:

x = seq(from=0, to=9, by=0.05)
y = sin(x)

How do I plot the integral from 0 to x over the interval, say, 0 to 10? Where integral is the area bounded by the curve and y=0.

This of course should look very much like a plot of 1 - cos(x), but let's assume we don't know what y = f(x) actually is.

The only thing I know how to do that seems to make sense is:

spl = smooth.spline(x, y)

However I don't know what to do next.

EDIT: this is not a duplicate of shading under a curve, for one thing areas below y=0 need to be subtracted, for another it's not about displaying shaded regions, but about constructing a function that is the integral...

Answer 1

@Maciej Pitucha's answer is good too, but I eventually muddled my way through what I was originally trying to do with smooth.spline(), and it seems to work better for my actual data.

test.x = seq(from=0, to=9, by=0.05)
test.y = sin(x)
spl = smooth.spline(y=test.y, x=test.x)
f = function(x) {predict(spl, x)$y}
f.int = function(x) {integrate(f, lower=0, upper=x)$value}
f.int.vec = Vectorize(f.int, vectorize.args='x')

plot(test.x, test.y, type="l", ylim = c(-1,2))
lines(test.x, 1-cos(test.x), col="red")
lines(test.x, f.int.vec(test.x), col="blue")
legend(x="bottomright", 
       col=c("black","red", "blue"), 
       legend=c("sin", "1-cos", "integral"),
       lty=1)