**Integration by using Dimensional Analysis can only be used for partial checking of integration. It will not give you the full answer.**

Take For example, consider the definite integral (and we will focus exclusively on definite integrals here)

**integration ∫**_{0}^{a}x^{5}dx (1)

If we consider x to have dimension of length, then the integrand has units of length^{5} but you have to include another power of length from dx, so the final answer must have units of length^{6}. The only nontrivial dimensionful constant in the problem is a, so the final answer must be proportional to a^{6}; the right answer, of course, is a^{6}/6.