Study the continuity of this function

[Felafel]

Homework Statement

f(x) = [x^2]sinπx, x ∈ R, being [x] the integer part of x

Homework Equations

The Attempt at a Solution

I'd say it's trivially continuos on all R, because it's the product of two continuos functions: y: = [x^2] and g: = sinπx.
However, being part of my analysis class homework (always a bit tricky to solve), it seems a bit too easy to me. So, i thought there might be something strange I haven't noticed. Or is my reasoning just correct?
thanks in advance!

 

[Dick]

Homework Statement

f(x) = [x^2]sinπx, x ∈ R, being [x] the integer part of x

Homework Equations

The Attempt at a Solution

I'd say it's trivially continuos on all R, because it's the product of two continuos functions: y: = [x^2] and g: = sinπx.
However, being part of my analysis class homework (always a bit tricky to solve), it seems a bit too easy to me. So, i thought there might be something strange I haven't noticed. Or is my reasoning just correct?
thanks in advance!

x^2 is continuous. The integer part of x^2 is not continuous.