Is There a Fundamental Theorem of Calculus for Squared Derivatives?

[Bruno Tolentino]

Fundamental theorem of calculus:\int_a^b \frac{df}{dx} dx = f(b) - f(a)
All right? Everybody knows...

BUT, BUT, exist some analog of the FTC for this case:

\int_a^b \left( \frac{df}{dx} \right)^2 dx = ?

Hum?

 

[Mark44]

Fundamental theorem of calculus:\int_a^b \frac{df}{dx} dx = f(b) - f(a)
All right? Everybody knows...

BUT, BUT, exist some analog of the FTC for this case:

\int_a^b \left( \frac{df}{dx} \right)^2 dx = ?

Not that I'm aware of.