I know that this a very juvenile question, but I began to doubt my understanding of the rule when reading this answer to another of my questions. So when looking at a Wizard's spells per day in Pathfinder, are the spells for each section the grand total of casts that the wizard has, or do all the casts between levels get added together? For instance, would a level 5 wizard have 3 first level spells per day, or would they have 11?
A 5th level wizard can cast 3 1st level spells per day.
When looking at a class table just look at the row for the level of your character, all other rows are ignored.
To figure out how many spells per day a character of a spell-casting class can cast, you consult the following information:
First, consult the row in their class table corresponding to their current level. A first-level Wizard can cast at least 3 1st-, 2 2nd-, and 1 3rd-level spell per day.
Add spells-per-day for exceptional ability scores. To cast any spells, a Wizard needs at least an Int of 11, but 16 or 18 would be more common. If we assume our example wizard has an intelligence of 16, he gains one each 1st-, 2nd-, and 3rd-level spell.
Finally, add spells-per-day for other class features, feats, and so on that grant them. (For example, specialist wizards get an additional spell of each level.) Let's assume that our example wizard is a universalist with a familiar rather than a bonded item and has no feats that change his spell slot selection.
So our example wizard can cast 4 1st-, 3 2nd-, and 2 3rd-level spells. But if all he wants to do is cast 1st-level spells all day, he has an important tactical option: he can prepare 1st-level spells in higher-level slots (CRB 218, 'Spell Slots').
Perhaps our wizard is too lazy to carry a whole bunch of loot out of the dungeon, and so he wants to cast as many floating disks as possible in a day. He could fill all nine of his slots with floating disk.