Fundamental Theorem of Calculus Part 1

Theorem

• Let $a,b\in R$, $a<b$
• If $f$ is cont on $[a,b]$
• $F$ is any Antiderivative of $f$ on $[a,b]$ Then, ${\int }_a^{b}f(x)dx=F(x){|}_b^a=F(b)-F(a)$

FTOC Part 1 Proof

• Fundamental Theorem of Calculus Part 1 Proof

Corrolaries

• Continuity Implies Integrable