# Calculus: Calculus, General Integration – #5543

Question: Let f be defined as follows: $$f\left( t \right)=1$$, for $$t<0$$; $$f\left( t \right)={{t}^{2}}+1$$, for $$0\le t\le 2$$; and $$f\left( t \right)=5$$, for t > 2

a) Determine the function

$F\left( x \right)=\int\limits_{0}^{x}{f\left( t \right)dt}$

for x on the real line

b) Where is F differentiable? Calculate F‘ where F is differentiable.