2. For the function, f x x2; 0ax < 1 x2 5; 1axa2 (a) Verify explicitly that 2 0 f x dx

2. For the function, f ðxÞ ¼

x2; 0ax < 1 x2 þ 5; 1axa2

(a) Verify explicitly that ð2 0 f ðxÞ dx ¼
ð1 0 x2 dx þ
ð2 1 ðx2 þ 5Þ dx ¼
23 3 ;
by demonstrating that the contribution of the terms in the Riemann sums containing the point x ¼ 1 converge to 0.

(b) Confirm that this conclusion is independent of the definition of f ð1Þ.