does the following make sense?

d/dx {integral of y^2 from -a to a (dx)} =0

=>

integral of d(y^2)/dx from -a to a (dx) =0

=>

integral of 2yy' from -a to a (dx) =0

=>

integral of yy' from -a to a (dx) =0

=>

integral of yy' from -a to a (dx) =integral of x from -a to a = 0

=>

yy'=x

??