beta.diff<-function(r1,r2,n1,n2,a=1,b=1){
f <- function(x,y) dbeta(x+y,a+r1,b+n1-r1)*dbeta(y,a+r2,b+n2-r2)
vf=Vectorize(f,vectorize.args = 'y')
pdf <- function(x) integrate(function(y) vf(x,y),-1,1)$value
pdf=Vectorize(pdf)
cdf=function(x) integrate(pdf,-1,x)$value
cdf=Vectorize(cdf)
invisible(list(pdf=pdf,cdf=cdf))
}

r1=0
r2=7
n1=389
n2=385
cdf=beta.diff(r1,r2,n1,n2)$cdf
cdf(0)