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.

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