What does the big F stand for in eqautions like f(x)-sinb=F(a)-F(b) ?? It's not like the little f in function.
Typically, textbooks discussing the Fundamental Theorem of Calculus refer to F(x) ("big F") as the antiderivative of f(x) ("little f"). *This link might help
"f(x)-sinb=F(a)-F(b)" makes no sense. Are you sure it wasn't something like [itex]\int_b^a f(x)dx= F(a)- F(b)[/itex]?
By convention, if we use a lower-case letter to denote a function, we use an upper-case letter to denote its anti-derivative. It's not something you have to do -- it's just something that people usually do because everyone else does it and it's convenient.
I've seen this used as follows f(x)=x^2 g(x)=x/2 F(x)=f(x)/(g(x) Other than that, doesn't ring a bell. EDIT: What math class did you see this in?
Did you mean to type anything else? I didn't see a closed parenthesis. If it is indeed so, then the F(x) you saw does not refer to any antiderivative, but simply f(x) / g(x). As Hurkyl said below, the antiderivative notation is simply convention, and not a strict rule of mathematics.
That is simply defining F(x) to be f(x)/g(x)- making it clear that the convention "F(x) is an anti-derivative of f(x)" is not being used!
Actually, I hereby declare that the following definition of F(x) is unique and unviolable: [tex]F(x)=\frac{\pi}{1+\frac{\pi}{1+\frac{x}{e+\pi}}}[/tex]