I plan to write my own php shopping cart

is there a way in which I can link the shopping cart to payment methods such
as paypal?

basically its for a project at university and i want to be able to allow
users to add items to the cart on my website, view a price etc, select
shipping and all of that, I then want them to be able to click "Checkout"
and be taken to paypal which will automatically bring a paypal page up
showing how much the user has to pay... is this at all possible?

i want to use paypal because its free dont want to go into merchant stuff
and everything just want it to link to paying my paypal account

is there a way anyone can you help??

TIA

Christo