hello guys!
thank u for the help, but u didnt understood what i need.
1st, it is a[i] cuz i want to sum 1 + x[i], for all i's not j.
but i've solved it! :)
like i said, my code is more complex, but, if you need to integrate several
functions in a loop, thats what you  should do:

w2 = seq(-1,-1/3,length=100)
ib = length(w2)

bin = w2[2] - w2[1]

w3 <- numeric(ib-1)

for (h in 1:ib-1)

        w3[h] = (w2[h] + w2[h+1])/2 
end

probt <- numeric(ib)
di2 <- numeric(ia)
a2 <- numeric(ia)

ic = ib-1

arealog <- numeric(ic) 
log_probt <- numeric(ic)

funcs <- list()
funcs[]

# loop through to define functions
for(i in 1:ic){

    funcName <- paste( 'func', i, sep = '' )

    func = paste('function(z){c/(Ho*sqrt(dens*(1+z)^3 +
(1-dens)*(1+z)^(3*(1+w3[', i,']))))}',sep = '')

    funcs[[funcName]] = eval(parse(text=func))
 
    }
end

for(j in 1:ic){

for(i in 1:ia){

        d2 = integrate(funcs[[j]], lower = 0, upper = z[i])
        di2[i] = d2[1]
        a2[i] = 1 + z[i]
        
        }
end
di2 = unlist(di2)
        dist2 = di2*a2
        mag2 = 5*log(dist2) + 25
        prob2 = (1/disp*sqrt(2*pi))*exp( - ((mag2 - probv)^2)/2*disp^2)
        log_prob2 = log(prob2)
        log_proba2 = sum(log_prob2)
        log_probt[j] = log_proba2
        arealog[j] = bin*(log_proba2)   
        }
end

log_probt2 = sum(arealog)/(w2[ib] - w2[1])
  


 



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