Consider the function and the piecewise-defined function

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the function

f(x)=\begin{cases}2x, & x\le 1\\2,& x>1\end{cases}

and the piecewise-defined function

F(x)=\begin{cases}x^{2}+a, & x\le 1\\2x+b,& x>1\end{cases}

, where

a

and

b

are real constants. Find the values of

a

and

b

such that

F

is an antiderivative of

f

\mathbb{R}

and

F(1)=4