Pg. 202
Bonus Action: A spell cast with a bonus action is especially swift. You must use a bonus action on your turn to cast the spell, provided that you haven't already taken a bonus action this turn. You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
This is the only section that governs how many spells one can cast within your turn. Otherwise, all spells follow beneath the Cast a Spell action which, being an entire action, would limit a person to 1 such spell during their turn. But if a person gets another action, they can use that extra action to cast another spell.
What I'm confused about are Spell Attacks and their functioning with Extra Attacks.
Attack Pg. 192
With this action, you make one melee or ranged attack. See the "Making an Attack" section for the rules that govern attacks.
Making an Attack Pg. 193
Whether you're striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.
... If there's ever any question whether something you're doing counts as an attack, the rule is simple: If you're making an attack roll, you're making an attack.
My original understanding of RAW regarding spells with attack rolls was that they follow under the Cast a Spell action, so an Eldritch Knight that casts Firebolt is using his action to Cast a Spell, not take the Attack Action, preventing him from using Extra Attack.
But if Firebolt is considered an Attack, then by the above rules one may be able to reason that one can substitute Firebolt in for attacks in the Attack action, and since there is no rule that specifically states that one can only cast 1 spell in a given turn, then a Level 17 Eldritch Knight could cast 3 Firebolts using 1 Attack Action, potentially dealing 12d10 damage. Which seems wrong to me considering a non-casting 17th level Fighter is limited to dealing up to 6d6 + (3 x mod), assuming greatsword.
/u/JamesMusicus /u/brail or any others, help me out on this?