Quick question on integral calculation

[matts0]

Homework Statement

Hello, I have a question from my textbook on integral calculation. It's
Find f(pi/2) from the following information.
(i) f is positive and continuous.
(ii) the area under the curve y=f(x) from x=0 to x=a is a²+(a/2)*sin(a)+(π/2 )*cosa

So I think the second condition implies
F(a)-F(0) = a²+(a/2)*sin(a)+(π/2 )*cosa (F is the antiderivate of f)
But if I let a=0, I find the lefthand side of the equation will be 0 but the righthand side will be π/2 .
So please someone tell me where I made a mistake which seems to be quite a silly one.
Thanks in advance.

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Hammie]

Did you calculate the derivative?

 

[Ray Vickson]

Either you copied the question incorrectly or else the book has written an incorrect question. You are right: the two sides are different in the limit a-->0.

RGV