Question: Fundamental theorem of calculus

Hello people in mapleprime,

Though I wrote the title as Fundamental theorem of calculus,

what I am considering is just how to continue the chain of codes in calculation.

restart;

#I defined F__0 as

F__0:=x->Int(f(t),t=a..x);

#Then, the difference between a primitive function of f(x), F(x), and F__0 is no more than a constant C, so I write.

bb:=F(x)-F__0(x)=C;

#Then, substituting "a" into equation "bb", I obtain the value of F(a)

bb1:=subs(x=a,bb):cc:=simplify(%);

#Then, I substituted the value of C in "bb1" into "bb,"  obtaining the following "cc1."

cc1:=subs(isolate(cc,C),bb);

#And, then, I isolated the term of Int(f(t),t=a..x)  in cc1,

dd:=isolate(cc1,Int(f(t), t = a .. x));

#And, then, I substitute x=b into the outcome of dd, and obtain the final equation.

subs(x=b,dd);

Surely, with the above code, I could get the fundamental theorem. But, it looks in a little roundabout way.

So, I thought I would ask here about whether there aren't any better ways to do the fundamentally the same thing or

hints to improve the above code.

Please teach me about this.

Thanks in advance.

taro