In I.S.I.’s B.Stat Entrance 2005, the following problem appeared:

**Problem:** Let $$ f(x) = \int_0^1 |t-x|t dt $$ for all real x. Sketch the graph of f(x). What is the minimum value of f(x)?

Here is the first installment of a discussion on that.

### Part 1

### Part 2

Scheduled on 30th Decemeber 2017