I did try installing fglrx, but the latest driver isn't compatible with my graphics card, and the older drivers doesn't support my X server and kernel...
(That DKMS compile error!)

I am using Ubuntu 13.04 with Hybrid ATI/Intel graphics.

lspci? here it is:

00:00.0 Host bridge: Intel Corporation 3rd Gen Core processor DRAM Controller (rev 09)
00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v2/3rd Gen Core processor PCI Express Root Port (rev 09)
00:02.0 VGA compatible controller: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09)
00:14.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB xHCI Host Controller (rev 04)
00:16.0 Communication controller: Intel Corporation 7 Series/C210 Series Chipset Family MEI Controller #1 (rev 04)
00:1a.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #2 (rev 04)
00:1b.0 Audio device: Intel Corporation 7 Series/C210 Series Chipset Family High Definition Audio Controller (rev 04)
00:1c.0 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 1 (rev c4)
00:1c.3 PCI bridge: Intel Corporation 7 Series/C210 Series Chipset Family PCI Express Root Port 4 (rev c4)
00:1d.0 USB controller: Intel Corporation 7 Series/C210 Series Chipset Family USB Enhanced Host Controller #1 (rev 04)
00:1f.0 ISA bridge: Intel Corporation HM76 Express Chipset LPC Controller (rev 04)
00:1f.2 SATA controller: Intel Corporation 7 Series Chipset Family 6-port SATA Controller [AHCI mode] (rev 04)
00:1f.3 SMBus: Intel Corporation 7 Series/C210 Series Chipset Family SMBus Controller (rev 04)
01:00.0 Display controller: Advanced Micro Devices [AMD] nee ATI Mars [Radeon HD 8670A/8750M]
02:00.0 Network controller: Intel Corporation Centrino Advanced-N 6235 (rev 24)
03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168 PCI Express Gigabit Ethernet controller (rev 06)

Well, but BOINC seems to be not compatible with open source drivers, just fglrx.

BOINC client uses proprietary library and that OpenCL, CUDA, and CAL, which none of them is open source and not supported by my graphics card.

Nice, 3d games are able to run on my computer, btw.

Well, but BOINC seems to be not compatible with open source drivers, just fglrx.

BOINC client uses proprietary library and that OpenCL, CUDA, and CAL, which none of them is open source and not supported by my graphics card.

Nice, 3d games are able to run on my computer, btw.

BOINC doesn't care about vendors. All that matters is that the drivers you use support whatever technology you try to use.

Open source drivers don't currently support OpenCL, CUDA or CAL. (Thought OpenCL support appears to be under work. Don't know about the other two.)

Being able to play 3D games is irrelevant here.