Q: Let f:[0,2] -> R be defined by f(x) =( 1+x, x<=1 ) ( x^2, x>1). Then f is integrabe, but not continuous. Define F(x) = int (upper=x, lower=0) f(t)dt. Determine if F'(1) exist.
a) Evaluate lim (x->1+) {F(x)-F(1)}/(x-1)
b) Evaluate lim (x->1-) {F(x)-F(1)}/(x-1)
c) Does F'(1) exist? What is its value?