function integrand(x) { return (Math.exp(x)); } ;

var from=0 ;
var to=1 ;
var accuracy=0.001 ; // or whatever

var acc2=accuracy/Math.abs(to-from) ;
var sum=0 ;
var ordinates=0;

function adaptive (from, to) {
 var median =(to+from)/2 ;
 stepWidth=to-from ;
 low=integrand(from) ; 
 high=integrand(to) ;
 trapezoid=(low+high)*stepWidth/2 ;
 Simpson=(low+high+4*integrand(median))*stepWidth/6 ;
 errMargin=acc2*Math.abs(stepWidth) ;
 if (Math.abs(Simpson-trapezoid)<errMargin)
  {sum+=Simpson ; ordinates++ ; }
 else { adaptive(from,median); adaptive(median, to);} ;} ;

adaptive (from, to);
alert("Integral value: "+sum+" after "+ordinates+" ordinates.");