Definite integral gives solution involving Pi, is this result exact?

Mathematica novice here. When I compute the integral

Integrate[ Sin[x] Sin[3*x] Cos[2*y] / (Sin[x] ^2 + Cos [y]^2) , {x, 0, Pi}, {y, 0, Pi}]

I receive the output
$$ frac{pi}{2} (pi – 4)$$

Does the fact that the output is a function of Pi (instead of, say, $-1.3484…$) mean that NIntegrate was not used, and the result was computed exactly?

And if so, is there a way of receiving a "step by step" computation?
WolframAlpha["Integrate[ Sin[x] Sin[3*x] Cos[2*y] / (Sin[x] ^2 + Cos [y]^2) , {x, 0, Pi}, {y, 0, Pi}]" fails to understand the query…