Mainstream “mathematicians” have never understood the fundamental theorem of calculus (ftoc) because they have never understood the Mean Value Theorem (mvt) from which the ftoc is directly derived in one step. The reason for this is realised by the unremarkable statement of the mvt in mainstream texts.

f(b)-f(a)=f'(c)x(b-a)=\int_a^b f'(x) dx