Windows 7: Two questions.

First, how good is the Intel Core i3 m370 processor?
it is supposed to be fast, but my computer is slow...

Second, I constantly have to put my computer to sleep during the day, my question is if it can harm my computer life-time and performance?

1. question:
Please look at this performace benchmark chart.
PassMark CPU Benchmarks - High Mid Range CPU's
note: this is the high-mid range section, your cpu is at the 4st place here

2. question:
Well, when you put your computer to sleep (hibernating is not the same), it stores all your pending data in the RAM, which needs a little - but constant electricity to work. So the pc consumes power, ram and psu. But no other parts are being used.
Yes, it will shorten the life-time of your psu (and ram maybe), but it is not significant. Sleep mode is the same like running the computer, although it has a much smaller impact on life-time.

Thanks!

1. What are the other "ranges"?
2.Which parts are turned off when you put the computer to sleep? is it better to put it to sleep than to keep it running?

1. I mean you can swith btw different charts on your right (lower end, high end etc.), sorry if I was not using the proper word
2. every parts are turned off except:
-power supply unit (very low usage)
-ram is used in the same way when the system is running, and it uses a few volts
Yes, it's better t put it in sleep, than leave it running.

I see. Ty!

Now I have another problem, I have that microprocessor, and 2GB RAM and Intel HD Graphics, do you think it makes my comp slow

Almost anything can make acomputer slow, but I you have a software issue.
(However you may want to consider upgrading to 4gB of ram)
You should have a good antimalware&firewall software. G-data, kapersky, norton are best ones, but there are free ones too (like Avira).
So scan your system looking 4 viruses with a software.

When done, and if nothing was found, open task manager (CtrlAltDel is the easiest way) and look for processe that are using more than 10% of your cpu capacity.
In case you found some, that you don't know what they are, let me know about that. (even if they seem to be system processes)

My laptop is new...anyway I want to know more about my integrated graphics card(or should I say chip)

My memory:
Memory Type DDR3 (PC3-8500F)
Speed 533 MHz (DDR3 1066)

What is "1066"?
What is "(PC3-8500F)"
533MHz is speed I guess, isn't is slow?

The integrated graphics is ok for viewing pictures or videos. But if you try to play games with it, forget it. And how do you define "slow" - how does this slowness manifest itself?

But when you say games, what games exactly? - I find it is really slow even on flash/shockwave/online videos...so on...

Slow I mean I see speedgamer01 memory 8GB 1600MHz DDR3 Hyper
1600MHz and 533Mhz...And maybe its a different channel architecture

Anything on-line may be a line problem rather than a system problem. You would have to define the problems in much more detail to shed some light.