Wired Intelligent Edge

I have 2 routers and two diffrent ISP on each connected to a HP core 2824 as the main switch. I want to utilize both ISP. for example, I want some internet traffic to go to router 1(ISP1)  and certain website to router 2 (ISP2). how do I achieve this.

You would need to do it on the routers as I strongly suspect the 2824 can't do any kind of routing.

Either that, or, you could replace the 2824 with a Layer3 switch.

Looks like I lied: The "Advanced Traffic Management Guide" for the 2800 has a Chapter 7 "IP Routing Features" which starts off:

The switches covered in this guide offer IP static routing, supporting up to 16 static routes. IP static routing is configurable through the switch’s console CLI. This chapter refers the switch as a “routing switch”. When IP routing is enabled on your switch, it behaves just like any other IP router. Basic IP routing configuration consists of adding IP addresses and enabling IP routing. For configuring the IP addresses, see chapter 7, “Configuring IP Addresses”. 

So it looks like you can configure static routes on your 2824.

Still, trying to sort web traffic out by target IP address won't really work unless the target website exists in its own little bubble. 

Realistically, if you want to make use of both routers, you'll probably have your internal hosts split up by VLAN, and have each VLAN's default GW address sitting on one of the routers, and make each router route for half the VLANs.

If your routers support VRRP, then great, you can make this work quite well, otherwise configuring some kind of resilience for your internet access could be a bit fiddly.